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Automated Classifier Selection with Bayesian and ASHA Optimization

This example shows how to use fitcauto to automatically try a selection of classification model types with different hyperparameter values, given training predictor and response data. By default, the function uses Bayesian optimization to select and assess models. If your training data set contains many observations, you can use an asynchronous successive halving algorithm (ASHA) instead. After the optimization is complete, fitcauto returns the model, trained on the entire data set, that is expected to best classify new data. Check the model performance on test data.

Load Sample Data

This example uses the 1994 census data stored in census1994.mat. The data set consists of demographic information from the US Census Bureau that can be used to predict whether an individual makes over $50,000 per year.

Load the sample data census1994, which contains the training data adultdata and the test data adulttest. Preview the first few rows of the training data set.

load census1994
head(adultdata)
ans=8×15 table
    age       workClass          fnlwgt      education    education_num       marital_status           occupation        relationship     race      sex      capital_gain    capital_loss    hours_per_week    native_country    salary
    ___    ________________    __________    _________    _____________    _____________________    _________________    _____________    _____    ______    ____________    ____________    ______________    ______________    ______

    39     State-gov                77516    Bachelors         13          Never-married            Adm-clerical         Not-in-family    White    Male          2174             0                40          United-States     <=50K 
    50     Self-emp-not-inc         83311    Bachelors         13          Married-civ-spouse       Exec-managerial      Husband          White    Male             0             0                13          United-States     <=50K 
    38     Private             2.1565e+05    HS-grad            9          Divorced                 Handlers-cleaners    Not-in-family    White    Male             0             0                40          United-States     <=50K 
    53     Private             2.3472e+05    11th               7          Married-civ-spouse       Handlers-cleaners    Husband          Black    Male             0             0                40          United-States     <=50K 
    28     Private             3.3841e+05    Bachelors         13          Married-civ-spouse       Prof-specialty       Wife             Black    Female           0             0                40          Cuba              <=50K 
    37     Private             2.8458e+05    Masters           14          Married-civ-spouse       Exec-managerial      Wife             White    Female           0             0                40          United-States     <=50K 
    49     Private             1.6019e+05    9th                5          Married-spouse-absent    Other-service        Not-in-family    Black    Female           0             0                16          Jamaica           <=50K 
    52     Self-emp-not-inc    2.0964e+05    HS-grad            9          Married-civ-spouse       Exec-managerial      Husband          White    Male             0             0                45          United-States     >50K  

Each row contains the demographic information for one adult. The last column salary shows whether a person has a salary less than or equal to $50,000 per year or greater than $50,000 per year.

Use Automated Model Selection with Bayesian Optimization

Find an appropriate classifier for the data in adultdata by using fitcauto. By default, fitcauto uses Bayesian optimization to select models and their hyperparameter values, and computes the cross-validation classification error (Validation loss) for each model. By default, fitcauto provides a plot of the optimization and an iterative display of the optimization results. For more information on how to interpret these results, see Verbose Display.

Set the observation weights, try all available learner types and hyperparameters, and specify to run the Bayesian optimization in parallel, which requires Parallel Computing Toolbox™. Due to the nonreproducibility of parallel timing, parallel Bayesian optimization does not necessarily yield reproducible results. Because of the complexity of the optimization, this process can take some time, especially for larger data sets.

bayesianOptions = struct("UseParallel",true);
[bayesianMdl,bayesianResults] = fitcauto(adultdata,"salary","Weights","fnlwgt", ...
    "Learners","all","OptimizeHyperparameters","all", ...
    "HyperparameterOptimizationOptions",bayesianOptions);
Warning: 'CategoricalPredictors' value must be empty or 'all' for a 'knn' learner. The function omits 'knn' from the list of learners.
Warning: Categorical predictors are not supported for a 'discr' learner. The function omits 'discr' from the list of learners.
Warning: Data set has more than 10000 observations. Because ASHA optimization often finds good solutions faster than Bayesian optimization for data sets with many observations, try specifying the 'Optimizer' field value as 'asha' in the 'HyperparameterOptimizationOptions' value structure.
Warning: It is recommended that you first standardize all numeric predictors when optimizing the Naive Bayes 'Width' parameter. Ignore this warning if you have done that.
Starting parallel pool (parpool) using the 'local' profile ...
Connected to the parallel pool (number of workers: 6).
Copying objective function to workers...
Done copying objective function to workers.
Learner types to explore: ensemble, kernel, linear, nb, svm, tree
Total iterations (MaxObjectiveEvaluations): 180
Total time (MaxTime): Inf

|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|    1 |       6 | Best   |    0.17115 |            4.1409 |         0.17115 |         0.17115 |         tree | MinLeafSize:           1308 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:           129 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     9 |
|    2 |       6 | Error  |        NaN |            5.8369 |         0.17115 |         0.17115 |          svm | BoxConstraint:    0.0039078 |
|      |         |        |            |                   |                 |                 |              | KernelScale:      0.0041503 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          4 |
|      |         |        |            |                   |                 |                 |              | Standardize:          false |
|    3 |       6 | Accept |    0.21702 |            2.7086 |         0.17115 |         0.17115 |       linear | Lambda:           0.0002108 |
|      |         |        |            |                   |                 |                 |              | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | Regularization:       ridge |
|    4 |       6 | Accept |    0.18989 |            6.0701 |         0.17115 |         0.17115 |       linear | Lambda:            0.051636 |
|      |         |        |            |                   |                 |                 |              | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | Regularization:       ridge |
|    5 |       6 | Accept |    0.24677 |            42.561 |         0.17115 |         0.17115 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | KernelScale:        0.11479 |
|      |         |        |            |                   |                 |                 |              | Lambda:          0.00051256 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:3144 |
|    6 |       6 | Best   |     0.1622 |            1.6833 |          0.1622 |          0.1622 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|      |         |        |            |                   |                 |                 |              | Kernel:         <undefined> |
|    7 |       6 | Accept |    0.23856 |            48.252 |          0.1622 |          0.1622 |     ensemble | Method:            RUSBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      278 |
|      |         |        |            |                   |                 |                 |              | LearnRate:          0.04363 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           9467 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:            13 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|    8 |       6 | Accept |    0.17169 |            53.236 |          0.1622 |          0.1622 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      190 |
|      |         |        |            |                   |                 |                 |              | LearnRate:         0.009595 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           4927 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:          1659 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|    9 |       6 | Accept |    0.25327 |            22.206 |          0.1622 |          0.1622 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | KernelScale:       0.019076 |
|      |         |        |            |                   |                 |                 |              | Lambda:          8.2128e-08 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions: 903 |
|   10 |       6 | Best   |    0.14083 |            46.045 |         0.14083 |          0.1622 |     ensemble | Method:          AdaBoostM1 |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:       51 |
|      |         |        |            |                   |                 |                 |              | LearnRate:         0.010501 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:            264 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:         10796 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   11 |       6 | Accept |    0.24677 |            49.785 |         0.14083 |          0.1622 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | KernelScale:       0.012471 |
|      |         |        |            |                   |                 |                 |              | Lambda:          6.2848e-08 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:4735 |
|   12 |       6 | Accept |    0.18178 |            112.83 |         0.14083 |         0.17115 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               531.86 |
|      |         |        |            |                   |                 |                 |              | Kernel:              normal |
|   13 |       6 | Accept |    0.22245 |            1.5098 |         0.14083 |         0.17115 |       linear | Lambda:          5.2257e-08 |
|      |         |        |            |                   |                 |                 |              | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | Regularization:       lasso |
|   14 |       6 | Accept |    0.23856 |             37.43 |         0.14083 |         0.17115 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      257 |
|      |         |        |            |                   |                 |                 |              | LearnRate:        0.0022309 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           8893 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:             6 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   15 |       6 | Accept |    0.16386 |             6.977 |         0.14083 |         0.17115 |       linear | Lambda:          1.2971e-06 |
|      |         |        |            |                   |                 |                 |              | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | Regularization:       ridge |
|   16 |       6 | Accept |      0.148 |             177.2 |         0.14083 |         0.17115 |          svm | BoxConstraint:       5.3771 |
|      |         |        |            |                   |                 |                 |              | KernelScale:         13.172 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   17 |       6 | Accept |    0.19972 |            30.992 |         0.14083 |         0.17115 |     ensemble | Method:            RUSBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:       61 |
|      |         |        |            |                   |                 |                 |              | LearnRate:        0.0022005 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:            249 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:           658 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   18 |       6 | Accept |     0.1622 |            0.4573 |         0.14083 |          0.1669 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|      |         |        |            |                   |                 |                 |              | Kernel:         <undefined> |
|   19 |       6 | Best   |    0.13106 |            68.692 |         0.13106 |          0.1669 |     ensemble | Method:         GentleBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      167 |
|      |         |        |            |                   |                 |                 |              | LearnRate:          0.87924 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:              9 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:             5 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   20 |       6 | Error  |        NaN |             2.415 |         0.13106 |          0.1669 |          svm | BoxConstraint:       2.7183 |
|      |         |        |            |                   |                 |                 |              | KernelScale:       0.044663 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          4 |
|      |         |        |            |                   |                 |                 |              | Standardize:          false |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   21 |       6 | Accept |    0.14471 |            1.3765 |         0.13106 |         0.15793 |         tree | MinLeafSize:            104 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:          5184 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     8 |
|   22 |       6 | Accept |    0.19853 |            79.147 |         0.13106 |         0.15793 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:                45514 |
|      |         |        |            |                   |                 |                 |              | Kernel:                 box |
|   23 |       6 | Accept |     0.2467 |            12.256 |         0.13106 |         0.15793 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | KernelScale:        0.14114 |
|      |         |        |            |                   |                 |                 |              | Lambda:          2.8324e-06 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions: 350 |
|   24 |       6 | Accept |    0.24677 |             228.2 |         0.13106 |         0.15793 |          svm | BoxConstraint:     0.016454 |
|      |         |        |            |                   |                 |                 |              | KernelScale:         195.62 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   25 |       6 | Accept |    0.22584 |           0.81299 |         0.13106 |         0.17105 |         tree | MinLeafSize:           3819 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:           909 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     2 |
|   26 |       6 | Accept |    0.14896 |            54.975 |         0.13106 |         0.17031 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:              0.50222 |
|      |         |        |            |                   |                 |                 |              | Kernel:            triangle |
|   27 |       6 | Accept |    0.13859 |            39.098 |         0.13106 |         0.17031 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | KernelScale:          38.43 |
|      |         |        |            |                   |                 |                 |              | Lambda:          1.4954e-06 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions: 239 |
|   28 |       6 | Accept |    0.16354 |            6.2686 |         0.13106 |         0.17031 |       linear | Lambda:          2.2757e-05 |
|      |         |        |            |                   |                 |                 |              | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | Regularization:       ridge |
|   29 |       6 | Accept |    0.22319 |            1.1041 |         0.13106 |         0.17031 |       linear | Lambda:          3.0618e-09 |
|      |         |        |            |                   |                 |                 |              | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | Regularization:       lasso |
|   30 |       6 | Accept |    0.22319 |           0.96159 |         0.13106 |         0.17031 |       linear | Lambda:          7.5579e-09 |
|      |         |        |            |                   |                 |                 |              | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | Regularization:       lasso |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   31 |       6 | Accept |    0.32931 |            249.56 |         0.13106 |         0.17031 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | KernelScale:        0.32143 |
|      |         |        |            |                   |                 |                 |              | Lambda:          6.0283e-07 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:5258 |
|   32 |       6 | Accept |    0.13628 |            29.765 |         0.13106 |         0.15473 |     ensemble | Method:                 Bag |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:       21 |
|      |         |        |            |                   |                 |                 |              | LearnRate:              NaN |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:              9 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:         10267 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:    12 |
|   33 |       6 | Accept |     0.1622 |           0.42231 |         0.13106 |         0.15473 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|      |         |        |            |                   |                 |                 |              | Kernel:         <undefined> |
|   34 |       6 | Accept |    0.22245 |           0.81185 |         0.13106 |         0.15473 |       linear | Lambda:          0.00036246 |
|      |         |        |            |                   |                 |                 |              | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | Regularization:       lasso |
|   35 |       6 | Accept |     0.1555 |           0.63361 |         0.13106 |         0.15473 |         tree | MinLeafSize:            120 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:           200 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     3 |
|   36 |       6 | Accept |     0.1622 |           0.37218 |         0.13106 |         0.15473 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|      |         |        |            |                   |                 |                 |              | Kernel:         <undefined> |
|   37 |       6 | Accept |    0.23856 |           0.29699 |         0.13106 |         0.15473 |         tree | MinLeafSize:           8766 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:             9 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     6 |
|   38 |       6 | Best   |     0.1286 |            87.205 |          0.1286 |          0.1453 |     ensemble | Method:         GentleBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      330 |
|      |         |        |            |                   |                 |                 |              | LearnRate:        0.0098276 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:             12 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:             3 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   39 |       6 | Accept |    0.24685 |            4.3779 |          0.1286 |          0.1453 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | KernelScale:         1.7072 |
|      |         |        |            |                   |                 |                 |              | Lambda:          4.9189e-08 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions: 186 |
|   40 |       6 | Accept |    0.19477 |            104.34 |          0.1286 |          0.1453 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               7640.9 |
|      |         |        |            |                   |                 |                 |              | Kernel:            triangle |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   41 |       6 | Accept |    0.15967 |            59.354 |          0.1286 |         0.14561 |     ensemble | Method:         GentleBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      383 |
|      |         |        |            |                   |                 |                 |              | LearnRate:         0.038324 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           7227 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:          2177 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   42 |       6 | Accept |     0.1622 |            1.0952 |          0.1286 |         0.14561 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|      |         |        |            |                   |                 |                 |              | Kernel:         <undefined> |
|   43 |       6 | Accept |     0.1849 |             441.8 |          0.1286 |         0.14561 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | KernelScale:         559.78 |
|      |         |        |            |                   |                 |                 |              | Lambda:          8.2254e-06 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:7841 |
|   44 |       6 | Accept |    0.23856 |           0.90498 |          0.1286 |         0.14561 |         tree | MinLeafSize:          11397 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:             6 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     2 |
|   45 |       6 | Accept |    0.21702 |            1.8862 |          0.1286 |         0.14561 |       linear | Lambda:          0.00031752 |
|      |         |        |            |                   |                 |                 |              | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | Regularization:       ridge |
|   46 |       6 | Accept |    0.15113 |           0.64593 |          0.1286 |         0.14561 |         tree | MinLeafSize:             15 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:            18 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:    10 |
|   47 |       6 | Accept |    0.22319 |            1.0114 |          0.1286 |         0.14561 |       linear | Lambda:           0.0079609 |
|      |         |        |            |                   |                 |                 |              | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | Regularization:       lasso |
|   48 |       6 | Accept |    0.21702 |             1.183 |          0.1286 |         0.14561 |       linear | Lambda:            0.014859 |
|      |         |        |            |                   |                 |                 |              | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | Regularization:       ridge |
|   49 |       6 | Accept |    0.22319 |            1.0524 |          0.1286 |         0.14561 |       linear | Lambda:          9.0307e-10 |
|      |         |        |            |                   |                 |                 |              | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | Regularization:       lasso |
|   50 |       6 | Accept |    0.18098 |            84.088 |          0.1286 |         0.14561 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               303.14 |
|      |         |        |            |                   |                 |                 |              | Kernel:        epanechnikov |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   51 |       6 | Accept |    0.18478 |            705.34 |          0.1286 |         0.14561 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | KernelScale:         685.59 |
|      |         |        |            |                   |                 |                 |              | Lambda:          6.5111e-06 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:2855 |
|   52 |       6 | Accept |    0.18133 |            82.973 |          0.1286 |         0.14561 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               358.05 |
|      |         |        |            |                   |                 |                 |              | Kernel:        epanechnikov |
|   53 |       6 | Accept |    0.14417 |            1.1731 |          0.1286 |         0.14561 |         tree | MinLeafSize:             20 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:         19194 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:    10 |
|   54 |       6 | Accept |    0.15351 |           0.48309 |          0.1286 |         0.14561 |         tree | MinLeafSize:             31 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:          9291 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     3 |
|   55 |       6 | Accept |    0.19079 |            7.3404 |          0.1286 |         0.14561 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | KernelScale:         9.1721 |
|      |         |        |            |                   |                 |                 |              | Lambda:          7.4579e-06 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions: 137 |
|   56 |       6 | Accept |    0.22245 |           0.92055 |          0.1286 |         0.14561 |       linear | Lambda:          1.3978e-06 |
|      |         |        |            |                   |                 |                 |              | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | Regularization:       lasso |
|   57 |       6 | Accept |     0.1622 |           0.63712 |          0.1286 |         0.14561 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|      |         |        |            |                   |                 |                 |              | Kernel:         <undefined> |
|   58 |       6 | Accept |    0.24677 |            198.23 |          0.1286 |         0.14561 |          svm | BoxConstraint:      0.11794 |
|      |         |        |            |                   |                 |                 |              | KernelScale:          604.2 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   59 |       6 | Accept |    0.15076 |           0.37789 |          0.1286 |         0.14561 |         tree | MinLeafSize:              5 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:           120 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     3 |
|   60 |       6 | Accept |    0.15376 |            0.5061 |          0.1286 |         0.14561 |         tree | MinLeafSize:              7 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:             8 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:    13 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   61 |       6 | Accept |    0.24677 |            14.057 |          0.1286 |         0.14561 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | KernelScale:       0.024719 |
|      |         |        |            |                   |                 |                 |              | Lambda:          7.8849e-06 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:1387 |
|   62 |       6 | Accept |    0.24677 |            12.415 |          0.1286 |         0.14561 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | KernelScale:        0.31491 |
|      |         |        |            |                   |                 |                 |              | Lambda:          4.0883e-08 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:1269 |
|   63 |       6 | Accept |    0.14477 |            98.657 |          0.1286 |         0.13884 |     ensemble | Method:         GentleBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      170 |
|      |         |        |            |                   |                 |                 |              | LearnRate:         0.099075 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           1462 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:          6219 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   64 |       6 | Accept |    0.15127 |            45.894 |          0.1286 |         0.14073 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:       23 |
|      |         |        |            |                   |                 |                 |              | LearnRate:          0.02095 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:              5 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:         12754 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   65 |       6 | Accept |    0.13527 |            53.795 |          0.1286 |         0.13986 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:       66 |
|      |         |        |            |                   |                 |                 |              | LearnRate:         0.090491 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:            579 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:          1206 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   66 |       6 | Accept |    0.13706 |            33.079 |          0.1286 |         0.13479 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:       45 |
|      |         |        |            |                   |                 |                 |              | LearnRate:         0.072253 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:             42 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:            28 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   67 |       6 | Accept |     0.1336 |            180.94 |          0.1286 |         0.13483 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      230 |
|      |         |        |            |                   |                 |                 |              | LearnRate:          0.11405 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:           1001 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:          2860 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   68 |       6 | Accept |    0.16092 |            183.16 |          0.1286 |         0.13483 |          svm | BoxConstraint:       4.9135 |
|      |         |        |            |                   |                 |                 |              | KernelScale:         109.99 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   69 |       6 | Accept |    0.12943 |            760.38 |          0.1286 |         0.13483 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | KernelScale:         17.218 |
|      |         |        |            |                   |                 |                 |              | Lambda:          2.9536e-07 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:5361 |
|   70 |       6 | Accept |    0.16712 |           0.49926 |          0.1286 |         0.13483 |         tree | MinLeafSize:            631 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:            38 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     3 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   71 |       6 | Accept |    0.15342 |            61.275 |          0.1286 |         0.13483 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:               3.9984 |
|      |         |        |            |                   |                 |                 |              | Kernel:        epanechnikov |
|   72 |       6 | Accept |    0.22319 |           0.97079 |          0.1286 |         0.13483 |       linear | Lambda:             0.57131 |
|      |         |        |            |                   |                 |                 |              | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | Regularization:       lasso |
|   73 |       6 | Accept |    0.26454 |            2391.5 |          0.1286 |         0.13483 |          svm | BoxConstraint:     0.010397 |
|      |         |        |            |                   |                 |                 |              | KernelScale:        0.26383 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   74 |       6 | Accept |    0.15591 |           0.42509 |          0.1286 |         0.13483 |         tree | MinLeafSize:            147 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:            30 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     4 |
|   75 |       6 | Accept |    0.30262 |            3188.9 |          0.1286 |         0.13483 |          svm | BoxConstraint:       4.5266 |
|      |         |        |            |                   |                 |                 |              | KernelScale:         4.4805 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |                 |              | Standardize:          false |
|   76 |       6 | Accept |    0.38172 |            2354.3 |          0.1286 |         0.13483 |          svm | BoxConstraint:      0.34479 |
|      |         |        |            |                   |                 |                 |              | KernelScale:        0.24179 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   77 |       6 | Accept |    0.17001 |             96.28 |          0.1286 |         0.13483 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |                 |              | Width:                   35 |
|      |         |        |            |                   |                 |                 |              | Kernel:              normal |
|   78 |       6 | Accept |    0.22319 |           0.97591 |          0.1286 |         0.13483 |       linear | Lambda:             0.65692 |
|      |         |        |            |                   |                 |                 |              | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | Regularization:       lasso |
|   79 |       6 | Accept |    0.13944 |            312.79 |          0.1286 |         0.13483 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | KernelScale:         109.29 |
|      |         |        |            |                   |                 |                 |              | Lambda:          4.7795e-06 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:2963 |
|   80 |       6 | Accept |     0.1461 |           0.80323 |          0.1286 |         0.13483 |         tree | MinLeafSize:             81 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:          4868 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     7 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   81 |       6 | Accept |     0.1622 |            1.0258 |          0.1286 |         0.13483 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |                 |              | Width:                  NaN |
|      |         |        |            |                   |                 |                 |              | Kernel:         <undefined> |
|   82 |       6 | Error  |        NaN |            2.1441 |          0.1286 |         0.13483 |          svm | BoxConstraint:     0.096689 |
|      |         |        |            |                   |                 |                 |              | KernelScale:        0.18876 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          4 |
|      |         |        |            |                   |                 |                 |              | Standardize:          false |
|   83 |       6 | Accept |    0.35552 |            2693.6 |          0.1286 |         0.13483 |          svm | BoxConstraint:     0.033837 |
|      |         |        |            |                   |                 |                 |              | KernelScale:       0.027074 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   84 |       6 | Accept |    0.14904 |           0.51977 |          0.1286 |         0.13483 |         tree | MinLeafSize:             29 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:            35 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:     7 |
|   85 |       6 | Accept |     0.2586 |            24.889 |          0.1286 |         0.13483 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |                 |              | KernelScale:      0.0010015 |
|      |         |        |            |                   |                 |                 |              | Lambda:          1.2767e-05 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:1350 |
|   86 |       6 | Accept |    0.55399 |            3398.7 |          0.1286 |         0.13483 |          svm | BoxConstraint:    0.0092124 |
|      |         |        |            |                   |                 |                 |              | KernelScale:         155.18 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |                 |              | Standardize:          false |
|   87 |       6 | Accept |     0.1831 |            199.67 |          0.1286 |         0.13483 |          svm | BoxConstraint:       8.6137 |
|      |         |        |            |                   |                 |                 |              | KernelScale:         204.69 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   88 |       6 | Accept |    0.13752 |            148.86 |          0.1286 |         0.13535 |     ensemble | Method:         GentleBoost |
|      |         |        |            |                   |                 |                 |              | NumLearningCycles:      293 |
|      |         |        |            |                   |                 |                 |              | LearnRate:          0.79452 |
|      |         |        |            |                   |                 |                 |              | MinLeafSize:             14 |
|      |         |        |            |                   |                 |                 |              | MaxNumSplits:             8 |
|      |         |        |            |                   |                 |                 |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |                 |              | NumVariablesToSample:   NaN |
|   89 |       6 | Accept |    0.16247 |            2925.9 |          0.1286 |         0.13535 |          svm | BoxConstraint:       290.56 |
|      |         |        |            |                   |                 |                 |              | KernelScale:         4.1671 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   90 |       6 | Accept |    0.16136 |            934.29 |          0.1286 |         0.13535 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |                 |              | KernelScale:         5.8589 |
|      |         |        |            |                   |                 |                 |              | Lambda:          1.4894e-06 |
|      |         |        |            |                   |                 |                 |              | NumExpansionDimensions:6076 |
|===========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Estimated min   | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | validation loss |              |                             |
|===========================================================================================================================================|
|   91 |       6 | Error  |        NaN |            2.1144 |          0.1286 |         0.13535 |          svm | BoxConstraint:       5.3542 |
|      |         |        |            |                   |                 |                 |              | KernelScale:      0.0016058 |
|      |         |        |            |                   |                 |                 |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |                 |              | Standardize:           true |
|   92 |       6 | Accept |    0.17756 |            1104.9 |          0.1286 |         0.13535 |       kernel | Learner:                svm |
|      |        ...

__________________________________________________________
Optimization completed.
Total iterations: 180
Total elapsed time: 17462.344 seconds
Total time for training and validation: 96919.4627 seconds

Best observed learner is an ensemble model with:
	Method:          LogitBoost
	NumLearningCycles:      307
	LearnRate:          0.66866
	MinLeafSize:              8
	MaxNumSplits:             6
	SplitCriterion: <undefined>
	NumVariablesToSample:   NaN
Observed validation loss: 0.12617
Time for training and validation: 114.7304 seconds

Best estimated learner (returned model) is an ensemble model with:
	Method:         GentleBoost
	NumLearningCycles:      235
	LearnRate:        0.0035794
	MinLeafSize:             68
	MaxNumSplits:             3
	SplitCriterion: <undefined>
	NumVariablesToSample:   NaN
Estimated validation loss: 0.12893
Estimated time for training and validation: 61.6123 seconds

Documentation for fitcauto display

The Total elapsed time value shows that the Bayesian optimization took a while to run (about 4.9 hours).

The final model returned by fitcauto corresponds to the best estimated learner. Before returning the model, the function retrains it using the entire training data set (adultdata), the listed Learner (or model) type, and the displayed hyperparameter values.

Use Automated Model Selection with ASHA Optimization

When fitcauto with Bayesian optimization takes a long time to run because of the number of observations in your training set, consider using fitcauto with ASHA optimization instead. Given that adultdata contains over 10,000 observations, try using fitcauto with ASHA optimization to automatically find an appropriate classifier. When you use fitcauto with ASHA optimization, the function randomly chooses several models with different hyperparameter values and trains them on a small subset of the training data. If the cross-validation classification error (Validation Loss) of a particular model is promising, the model is promoted and trained on a larger amount of the training data. This process repeats, and successful models are trained on progressively larger amounts of data. By default, fitcauto provides a plot of the optimization and an iterative display of the optimization results. For more information on how to interpret these results, see Verbose Display.

Set the observation weights, try all available learner types and hyperparameters, and specify to run the ASHA optimization in parallel. Note that ASHA optimization often has more iterations than Bayesian optimization by default. If you have a time constraint, you can specify the MaxTime field of the HyperparameterOptimizationOptions structure to limit the number of seconds fitcauto runs.

ashaOptions = struct("Optimizer","asha","UseParallel",true);
[ashaMdl,ashaResults] = fitcauto(adultdata,"salary","Weights","fnlwgt", ...
    "Learners","all","OptimizeHyperparameters","all", ...
    "HyperparameterOptimizationOptions",ashaOptions);
Warning: 'CategoricalPredictors' value must be empty or 'all' for a 'knn' learner. The function omits 'knn' from the list of learners.
Warning: Categorical predictors are not supported for a 'discr' learner. The function omits 'discr' from the list of learners.
Warning: It is recommended that you first standardize all numeric predictors when optimizing the Naive Bayes 'Width' parameter. Ignore this warning if you have done that.
Copying objective function to workers...
Warning: Files that have already been attached are being ignored. To see which files are attached see the 'AttachedFiles' property of the parallel pool.
Done copying objective function to workers.
Learner types to explore: ensemble, kernel, linear, nb, svm, tree
Total iterations (MaxObjectiveEvaluations): 2387
Total time (MaxTime): Inf

|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|    1 |       6 | Best   |     0.1833 |           0.52781 |          0.1833 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|    2 |       6 | Accept |    0.23405 |           0.57763 |          0.1833 |          102 |       linear | Lambda:          7.6648e-07 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|    3 |       6 | Accept |    0.22888 |           0.49975 |          0.1833 |          102 |       linear | Lambda:          0.00011257 |
|      |         |        |            |                   |                 |              |              | Learner:                svm |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|    4 |       6 | Accept |    0.19604 |            0.3835 |          0.1833 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|    5 |       6 | Accept |    0.21784 |           0.48395 |          0.1833 |          102 |       linear | Lambda:          1.8794e-07 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       ridge |
|    6 |       6 | Best   |    0.17277 |           0.38569 |         0.17277 |          408 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|    7 |       6 | Accept |    0.23373 |            0.5185 |         0.17277 |          102 |       linear | Lambda:          1.2608e-05 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|    8 |       6 | Accept |    0.25612 |            2.4452 |         0.17277 |          102 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | KernelScale:         11.254 |
|      |         |        |            |                   |                 |              |              | Lambda:            0.015724 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 326 |
|    9 |       6 | Accept |    0.21958 |            7.1669 |         0.17277 |          102 |          svm | BoxConstraint:       99.195 |
|      |         |        |            |                   |                 |              |              | KernelScale:         36.647 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   10 |       6 | Accept |    0.25909 |            8.1615 |         0.17277 |          102 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | KernelScale:      0.0034442 |
|      |         |        |            |                   |                 |              |              | Lambda:          7.2286e-07 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions:1549 |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|   11 |       6 | Best   |    0.16728 |           0.98305 |         0.16728 |          408 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   12 |       6 | Accept |    0.22845 |            8.7047 |         0.16728 |          102 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |              |              | KernelScale:         41.828 |
|      |         |        |            |                   |                 |              |              | Lambda:          7.5949e-08 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions:1767 |
|   13 |       6 | Accept |    0.69963 |            9.2306 |         0.16728 |          102 |          svm | BoxConstraint:       17.143 |
|      |         |        |            |                   |                 |              |              | KernelScale:         0.8188 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   14 |       6 | Accept |    0.23856 |           0.23818 |         0.16728 |          102 |         tree | MinLeafSize:           2581 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:             6 |
|      |         |        |            |                   |                 |              |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:     9 |
|   15 |       6 | Accept |    0.21089 |           0.51243 |         0.16728 |          408 |       linear | Lambda:          1.8794e-07 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       ridge |
|   16 |       6 | Accept |    0.24509 |            6.5163 |         0.16728 |          102 |          svm | BoxConstraint:     0.035345 |
|      |         |        |            |                   |                 |              |              | KernelScale:         70.734 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   17 |       6 | Accept |    0.24983 |            1.7456 |         0.16728 |          102 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | KernelScale:      0.0045787 |
|      |         |        |            |                   |                 |              |              | Lambda:           0.0057617 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 157 |
|   18 |       6 | Accept |    0.18862 |           0.28711 |         0.16728 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   19 |       6 | Accept |    0.25396 |            5.3202 |         0.16728 |          102 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |              |              | KernelScale:         1.5172 |
|      |         |        |            |                   |                 |              |              | Lambda:            0.018728 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 970 |
|   20 |       6 | Accept |    0.23856 |           0.21895 |         0.16728 |          102 |         tree | MinLeafSize:            120 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:            17 |
|      |         |        |            |                   |                 |              |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:     2 |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|   21 |       6 | Accept |    0.17237 |           0.40752 |         0.16728 |          408 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   22 |       6 | Accept |    0.22232 |           0.42795 |         0.16728 |          102 |       linear | Lambda:              2.9724 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|   23 |       6 | Best   |    0.16657 |           0.39947 |         0.16657 |         1629 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   24 |       6 | Accept |    0.22239 |            0.4554 |         0.16657 |          102 |       linear | Lambda:          2.7806e-05 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|   25 |       6 | Accept |     0.2952 |            8.0199 |         0.16657 |          102 |          svm | BoxConstraint:     0.050614 |
|      |         |        |            |                   |                 |              |              | KernelScale:         6.0247 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   26 |       6 | Error  |        NaN |            8.3248 |         0.16657 |          102 |          svm | BoxConstraint:       203.22 |
|      |         |        |            |                   |                 |              |              | KernelScale:        0.11329 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   27 |       6 | Accept |    0.18774 |            9.4024 |         0.16657 |          102 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               26.023 |
|      |         |        |            |                   |                 |              |              | Kernel:              normal |
|   28 |       5 | Accept |    0.24219 |            6.6727 |         0.16657 |          102 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | KernelScale:      0.0053538 |
|      |         |        |            |                   |                 |              |              | Lambda:          2.7097e-05 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions:1361 |
|   29 |       5 | Error  |        NaN |           0.33524 |         0.16657 |          102 |          svm | BoxConstraint:    0.0090329 |
|      |         |        |            |                   |                 |              |              | KernelScale:       0.024795 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          4 |
|      |         |        |            |                   |                 |              |              | Standardize:           true |
|   30 |       6 | Accept |    0.23282 |            7.4467 |         0.16657 |          102 |          svm | BoxConstraint:     0.099034 |
|      |         |        |            |                   |                 |              |              | KernelScale:      0.0086267 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |              |              | Standardize:           true |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|   31 |       6 | Accept |    0.21781 |            0.4873 |         0.16657 |          102 |       linear | Lambda:          5.4453e-06 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|   32 |       6 | Accept |    0.35809 |             1.404 |         0.16657 |          102 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |              |              | KernelScale:         1.7319 |
|      |         |        |            |                   |                 |              |              | Lambda:          0.00085629 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 104 |
|   33 |       6 | Accept |    0.21288 |           0.52465 |         0.16657 |          102 |       linear | Lambda:          0.00063782 |
|      |         |        |            |                   |                 |              |              | Learner:                svm |
|      |         |        |            |                   |                 |              |              | Regularization:       ridge |
|   34 |       6 | Accept |    0.17908 |            21.191 |         0.16657 |          102 |     ensemble | Method:         GentleBoost |
|      |         |        |            |                   |                 |              |              | NumLearningCycles:      377 |
|      |         |        |            |                   |                 |              |              | LearnRate:         0.027257 |
|      |         |        |            |                   |                 |              |              | MinLeafSize:             43 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:           329 |
|      |         |        |            |                   |                 |              |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:   NaN |
|   35 |       6 | Accept |    0.23856 |            13.827 |         0.16657 |          102 |     ensemble | Method:          AdaBoostM1 |
|      |         |        |            |                   |                 |              |              | NumLearningCycles:      238 |
|      |         |        |            |                   |                 |              |              | LearnRate:         0.022847 |
|      |         |        |            |                   |                 |              |              | MinLeafSize:          12916 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:            75 |
|      |         |        |            |                   |                 |              |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:   NaN |
|   36 |       6 | Accept |    0.18104 |             14.07 |         0.16657 |          102 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               3.1601 |
|      |         |        |            |                   |                 |              |              | Kernel:            triangle |
|   37 |       6 | Accept |    0.17248 |            15.368 |         0.16657 |          408 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               26.023 |
|      |         |        |            |                   |                 |              |              | Kernel:              normal |
|   38 |       6 | Accept |    0.20918 |           0.56712 |         0.16657 |          102 |       linear | Lambda:          0.00011269 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       ridge |
|   39 |       6 | Accept |    0.67983 |            22.722 |         0.16657 |          408 |          svm | BoxConstraint:       99.195 |
|      |         |        |            |                   |                 |              |              | KernelScale:         36.647 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   40 |       6 | Accept |    0.23856 |           0.23164 |         0.16657 |          102 |         tree | MinLeafSize:             62 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:            31 |
|      |         |        |            |                   |                 |              |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:     6 |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|   41 |       6 | Accept |    0.39265 |            2.4575 |         0.16657 |          102 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |              |              | KernelScale:        0.01949 |
|      |         |        |            |                   |                 |              |              | Lambda:          1.5679e-07 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 359 |
|   42 |       6 | Accept |    0.29263 |            1.7934 |         0.16657 |          102 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | KernelScale:         23.744 |
|      |         |        |            |                   |                 |              |              | Lambda:          7.6584e-08 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 116 |
|   43 |       6 | Accept |    0.21901 |            0.9797 |         0.16657 |          102 |       linear | Lambda:          1.2986e-06 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|   44 |       6 | Accept |    0.21196 |           0.43529 |         0.16657 |          102 |       linear | Lambda:          0.00013664 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|   45 |       6 | Accept |    0.18595 |           0.35076 |         0.16657 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   46 |       6 | Accept |    0.41729 |            22.162 |         0.16657 |          102 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |              |              | KernelScale:       0.013257 |
|      |         |        |            |                   |                 |              |              | Lambda:          7.0734e-08 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions:4800 |
|   47 |       6 | Best   |    0.16193 |           0.39629 |         0.16193 |          408 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   48 |       6 | Accept |    0.18519 |           0.41552 |         0.16193 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   49 |       6 | Accept |    0.35517 |            1.7655 |         0.16193 |          102 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |              |              | KernelScale:       0.001388 |
|      |         |        |            |                   |                 |              |              | Lambda:          3.1975e-07 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 193 |
|   50 |       6 | Accept |    0.22378 |           0.46214 |         0.16193 |          102 |       linear | Lambda:          3.5422e-08 |
|      |         |        |            |                   |                 |              |              | Learner:                svm |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|   51 |       6 | Accept |    0.18154 |           0.36808 |         0.16193 |          408 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   52 |       6 | Accept |    0.16863 |           0.36511 |         0.16193 |         1629 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   53 |       6 | Accept |    0.20281 |            2.5644 |         0.16193 |          102 |          svm | BoxConstraint:    0.0064229 |
|      |         |        |            |                   |                 |              |              | KernelScale:         958.04 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   54 |       6 | Accept |    0.23856 |           0.19664 |         0.16193 |          102 |         tree | MinLeafSize:           6412 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:            23 |
|      |         |        |            |                   |                 |              |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:     7 |
|   55 |       6 | Accept |    0.26397 |            4.1124 |         0.16193 |          102 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | KernelScale:          0.314 |
|      |         |        |            |                   |                 |              |              | Lambda:          2.2303e-06 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 694 |
|   56 |       6 | Accept |    0.17924 |            1.4097 |         0.16193 |          102 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |              |              | NumLearningCycles:       13 |
|      |         |        |            |                   |                 |              |              | LearnRate:          0.62696 |
|      |         |        |            |                   |                 |              |              | MinLeafSize:             24 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:           614 |
|      |         |        |            |                   |                 |              |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:   NaN |
|   57 |       6 | Best   |    0.15007 |            1.5243 |         0.15007 |          408 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |              |              | NumLearningCycles:       13 |
|      |         |        |            |                   |                 |              |              | LearnRate:          0.62696 |
|      |         |        |            |                   |                 |              |              | MinLeafSize:             24 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:           614 |
|      |         |        |            |                   |                 |              |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:   NaN |
|   58 |       6 | Accept |     0.2018 |            9.9532 |         0.15007 |          102 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               3.9538 |
|      |         |        |            |                   |                 |              |              | Kernel:              normal |
|   59 |       6 | Accept |    0.20213 |           0.39632 |         0.15007 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   60 |       6 | Accept |    0.25971 |            14.739 |         0.15007 |          102 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |              |              | KernelScale:        0.39803 |
|      |         |        |            |                   |                 |              |              | Lambda:          1.6745e-05 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions:3052 |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|   61 |       6 | Accept |    0.23856 |           0.18682 |         0.15007 |          102 |         tree | MinLeafSize:             59 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:          5359 |
|      |         |        |            |                   |                 |              |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:     2 |
|   62 |       6 | Accept |     0.1635 |            19.181 |         0.15007 |          408 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               3.1601 |
|      |         |        |            |                   |                 |              |              | Kernel:            triangle |
|   63 |       6 | Accept |    0.23856 |            5.9776 |         0.15007 |          102 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |              |              | NumLearningCycles:      111 |
|      |         |        |            |                   |                 |              |              | LearnRate:         0.083672 |
|      |         |        |            |                   |                 |              |              | MinLeafSize:           2980 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:          5832 |
|      |         |        |            |                   |                 |              |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:   NaN |
|   64 |       6 | Accept |    0.19308 |           0.28597 |         0.15007 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   65 |       6 | Accept |    0.16484 |            27.772 |         0.15007 |          408 |     ensemble | Method:         GentleBoost |
|      |         |        |            |                   |                 |              |              | NumLearningCycles:      377 |
|      |         |        |            |                   |                 |              |              | LearnRate:         0.027257 |
|      |         |        |            |                   |                 |              |              | MinLeafSize:             43 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:           329 |
|      |         |        |            |                   |                 |              |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:   NaN |
|   66 |       6 | Error  |        NaN |           0.33714 |         0.15007 |          102 |          svm | BoxConstraint:       4.6725 |
|      |         |        |            |                   |                 |              |              | KernelScale:       0.026549 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   67 |       6 | Accept |    0.25112 |            35.651 |         0.15007 |          102 |       kernel | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | KernelScale:      0.0096847 |
|      |         |        |            |                   |                 |              |              | Lambda:            0.020659 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions:7870 |
|   68 |       6 | Accept |    0.18534 |            8.9802 |         0.15007 |          102 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               135.21 |
|      |         |        |            |                   |                 |              |              | Kernel:                 box |
|   69 |       6 | Accept |    0.24933 |           0.66771 |         0.15007 |          102 |          svm | BoxConstraint:    0.0017712 |
|      |         |        |            |                   |                 |              |              | KernelScale:         10.315 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          4 |
|      |         |        |            |                   |                 |              |              | Standardize:           true |
|   70 |       6 | Accept |    0.21584 |             4.794 |         0.15007 |          102 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |              |              | KernelScale:         14.148 |
|      |         |        |            |                   |                 |              |              | Lambda:           0.0047599 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 886 |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|   71 |       6 | Accept |    0.20338 |           0.89738 |         0.15007 |          102 |       linear | Lambda:             0.19522 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|   72 |       6 | Accept |    0.17783 |           0.26471 |         0.15007 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   73 |       6 | Accept |     0.1734 |           0.36479 |         0.15007 |          408 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   74 |       6 | Best   |    0.13742 |            1.8412 |         0.13742 |         1629 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |              |              | NumLearningCycles:       13 |
|      |         |        |            |                   |                 |              |              | LearnRate:          0.62696 |
|      |         |        |            |                   |                 |              |              | MinLeafSize:             24 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:           614 |
|      |         |        |            |                   |                 |              |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:   NaN |
|   75 |       6 | Accept |    0.17481 |           0.30797 |         0.13742 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   76 |       6 | Accept |    0.21799 |           0.74319 |         0.13742 |          102 |       linear | Lambda:          1.1064e-07 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       ridge |
|   77 |       6 | Accept |    0.16922 |            14.713 |         0.13742 |          408 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               3.9538 |
|      |         |        |            |                   |                 |              |              | Kernel:              normal |
|   78 |       6 | Accept |    0.19186 |            9.4827 |         0.13742 |          102 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               21.308 |
|      |         |        |            |                   |                 |              |              | Kernel:        epanechnikov |
|   79 |       6 | Accept |    0.23856 |           0.17781 |         0.13742 |          102 |         tree | MinLeafSize:             72 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:           507 |
|      |         |        |            |                   |                 |              |              | SplitCriterion:    deviance |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:     1 |
|   80 |       6 | Accept |    0.21839 |           0.51905 |         0.13742 |          102 |       linear | Lambda:             0.19696 |
|      |         |        |            |                   |                 |              |              | Learner:                svm |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|   81 |       6 | Accept |    0.16708 |           0.56823 |         0.13742 |          408 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   82 |       6 | Accept |    0.22351 |           0.47201 |         0.13742 |          102 |       linear | Lambda:          1.0538e-05 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|   83 |       6 | Accept |    0.18091 |            14.968 |         0.13742 |          102 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               4583.9 |
|      |         |        |            |                   |                 |              |              | Kernel:            triangle |
|   84 |       6 | Error  |        NaN |           0.33319 |         0.13742 |          102 |          svm | BoxConstraint:       799.29 |
|      |         |        |            |                   |                 |              |              | KernelScale:       0.041631 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   85 |       6 | Accept |    0.21771 |           0.54034 |         0.13742 |          102 |       linear | Lambda:              2.9094 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       ridge |
|   86 |       6 | Accept |    0.22361 |           0.66518 |         0.13742 |          102 |       linear | Lambda:           0.0025068 |
|      |         |        |            |                   |                 |              |              | Learner:           logistic |
|      |         |        |            |                   |                 |              |              | Regularization:       ridge |
|   87 |       6 | Accept |    0.20679 |            8.4962 |         0.13742 |          102 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               0.4566 |
|      |         |        |            |                   |                 |              |              | Kernel:        epanechnikov |
|   88 |       6 | Accept |    0.16362 |            12.527 |         0.13742 |          408 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               135.21 |
|      |         |        |            |                   |                 |              |              | Kernel:                 box |
|   89 |       6 | Accept |    0.31314 |            2.4851 |         0.13742 |          102 |       kernel | Learner:                svm |
|      |         |        |            |                   |                 |              |              | KernelScale:        0.26268 |
|      |         |        |            |                   |                 |              |              | Lambda:          2.4658e-05 |
|      |         |        |            |                   |                 |              |              | NumExpansionDimensions: 287 |
|   90 |       6 | Accept |     0.1963 |           0.39621 |         0.13742 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|   91 |       6 | Accept |    0.29272 |            7.9575 |         0.13742 |          102 |          svm | BoxConstraint:     0.026874 |
|      |         |        |            |                   |                 |              |              | KernelScale:         3.5415 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   92 |       6 | Accept |    0.25432 |            9.0131 |         0.13742 |          102 |          svm | BoxConstraint:        329.7 |
|      |         |        |            |                   |                 |              |              | KernelScale:       0.017534 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   93 |       6 | Accept |    0.18366 |           0.36305 |         0.13742 |          102 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   94 |       6 | Accept |    0.21171 |            8.1838 |         0.13742 |          102 |          svm | BoxConstraint:     0.038505 |
|      |         |        |            |                   |                 |              |              | KernelScale:         1.8597 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   95 |       6 | Accept |     0.2473 |           0.62532 |         0.13742 |          102 |          svm | BoxConstraint:    0.0031518 |
|      |         |        |            |                   |                 |              |              | KernelScale:         64.038 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          3 |
|      |         |        |            |                   |                 |              |              | Standardize:           true |
|   96 |       6 | Accept |    0.16289 |            0.3975 |         0.13742 |          408 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   97 |       6 | Accept |     0.1624 |           0.37295 |         0.13742 |         1629 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|   98 |       6 | Accept |    0.25848 |            8.9384 |         0.13742 |          102 |          svm | BoxConstraint:    0.0025802 |
|      |         |        |            |                   |                 |              |              | KernelScale:       0.025276 |
|      |         |        |            |                   |                 |              |              | PolynomialOrder:          2 |
|      |         |        |            |                   |                 |              |              | Standardize:          false |
|   99 |       6 | Best   |    0.13168 |             4.284 |         0.13168 |         6513 |     ensemble | Method:          LogitBoost |
|      |         |        |            |                   |                 |              |              | NumLearningCycles:       13 |
|      |         |        |            |                   |                 |              |              | LearnRate:          0.62696 |
|      |         |        |            |                   |                 |              |              | MinLeafSize:             24 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:           614 |
|      |         |        |            |                   |                 |              |              | SplitCriterion: <undefined> |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:   NaN |
|  100 |       6 | Accept |    0.23856 |            1.5422 |         0.13168 |          102 |     ensemble | Method:          AdaBoostM1 |
|      |         |        |            |                   |                 |              |              | NumLearningCycles:       17 |
|      |         |        |            |                   |                 |              |              | LearnRate:         0.016685 |
|      |         |        |            |                   |                 |              |              | MinLeafSize:             43 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:           892 |
|      |         |        |            |                   |                 |              |              | SplitCriterion:         gdi |
|      |         |        |            |                   |                 |              |              | NumVariablesToSample:   NaN |
|========================================================================================================================================|
| Iter | Active  | Eval   | Validation | Time for training | Observed min    | Training set | Learner      | Hyperparameter:       Value |
|      | workers | result | loss       | & validation (sec)| validation loss | size         |              |                             |
|========================================================================================================================================|
|  101 |       6 | Accept |    0.22709 |           0.42263 |         0.13168 |          102 |       linear | Lambda:           6.792e-09 |
|      |         |        |            |                   |                 |              |              | Learner:                svm |
|      |         |        |            |                   |                 |              |              | Regularization:       lasso |
|  102 |       6 | Accept |    0.17125 |            13.985 |         0.13168 |          408 |           nb | DistributionNames:   kernel |
|      |         |        |            |                   |                 |              |              | Width:               21.308 |
|      |         |        |            |                   |                 |              |              | Kernel:        epanechnikov |
|  103 |       6 | Accept |    0.17426 |           0.38353 |         0.13168 |          408 |           nb | DistributionNames:   normal |
|      |         |        |            |                   |                 |              |              | Width:                  NaN |
|      |         |        |            |                   |                 |              |              | Kernel:         <undefined> |
|  104 |       6 | Accept |    0.18015 |           0.23257 |         0.13168 |          102 |         tree | MinLeafSize:              6 |
|      |         |        |            |                   |                 |              |              | MaxNumSplits:         17667 |
|      |         |        |            |    ...

__________________________________________________________
Optimization completed.
Total iterations: 2387
Total elapsed time: 2628.053 seconds
Total time for training and validation: 14609.748 seconds

Best observed learner is an ensemble model with:
	Method:          LogitBoost
	NumLearningCycles:      114
	LearnRate:          0.55256
	MinLeafSize:              5
	MaxNumSplits:            13
	SplitCriterion: <undefined>
	NumVariablesToSample:   NaN
Observed validation loss: 0.12429
Time for training and validation: 53.3034 seconds

Documentation for fitcauto display

The Total elapsed time value shows that the ASHA optimization took less time to run than the Bayesian optimization (about 0.7 hours).

The final model returned by fitcauto corresponds to the best observed learner. Before returning the model, the function retrains it using the entire training data set (adultdata), the listed Learner (or model) type, and the displayed hyperparameter values.

Evaluate Test Set Performance

Evaluate the performance of the returned bayesianMdl and ashaMdl models on the test set adulttest by using confusion matrices and receiver operating characteristic (ROC) curves.

For each model, find the predicted labels and score values for the test set.

[bayesianLabels,bayesianScores] = predict(bayesianMdl,adulttest);
[ashaLabels,ashaScores] = predict(ashaMdl,adulttest);

Create confusion matrices from the test set results. The diagonal elements indicate the number of correctly classified instances of a given class. The off-diagonal elements are instances of misclassified observations. Use a 1-by-2 tiled layout to compare the results.

tiledlayout(1,2)

nexttile
confusionchart(adulttest.salary,bayesianLabels)
title("Confusion Matrix (Bayesian Optimization)")

nexttile
confusionchart(adulttest.salary,ashaLabels)
title("Confusion Matrix (ASHA Optimization)")

Compute the test set classification accuracy for each model, where the accuracy is the percentage of correctly classified test set observations.

bayesianAccuracy = (1-loss(bayesianMdl,adulttest,"salary"))*100
bayesianAccuracy = 85.1825
ashaAccuracy = (1-loss(ashaMdl,adulttest,"salary"))*100
ashaAccuracy = 85.7155

Based on the confusion matrices and the accuracy values, ashaMdl slightly outperforms bayesianMdl on the test set. However, both models perform well.

For each model, plot the ROC curve for the score values corresponding to the label '<=50K'. Find the scores column that corresponds to that label. The column order of the scores matches the order of the classes in the trained model.

bayesianMdl.ClassNames
ans = 2×1 categorical
     <=50K 
     >50K 

ashaMdl.ClassNames
ans = 2×1 categorical
     <=50K 
     >50K 

Because '<=50K' is listed first for both models, the first column of the scores corresponds to that label.

Plot the ROC curves, and compute the area under the curve (AUC). The ROC curve shows the true positive rate versus the false positive rate for different thresholds of the classifier output. For a perfect classifier, whose true positive rate is always 1 regardless of the threshold, AUC = 1. For a binary classifier that randomly assigns observations to classes, AUC = 0.5. A large AUC value (close to 1) indicates good classifier performance.

[bayesianX,bayesianY,~,bayesianAUC] = perfcurve(adulttest.salary,bayesianScores(:,1),"<=50K");
[ashaX,ashaY,~,ashaAUC] = perfcurve(adulttest.salary,ashaScores(:,1),"<=50K");

figure
plot(bayesianX,bayesianY)
hold on
plot(ashaX,ashaY)
title("ROC Curves")
xlabel("False Positive Rate")
ylabel("True Positive Rate")
legend(["Bayesian Optimization","ASHA Optimization"])

bayesianAUC
bayesianAUC = 0.9026
ashaAUC
ashaAUC = 0.9084

Based on the AUC values, both classifiers perform well on the test data.

See Also

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Related Topics