# predict

Predict responses for new observations from ECOC incremental learning classification model

*Since R2022a*

## Description

specifies additional options using one or more name-value arguments. For example, specify
`label`

= predict(`Mdl`

,`X`

,`Name=Value`

)`ObservationsIn=columns`

to indicate that observations in the predictor
data are oriented along the columns of `X`

.

`[`

uses any of the input argument combinations in the previous syntaxes and additionally returns:`label`

,`NegLoss`

,`PBScore`

] = predict(___)

An array of negated average binary losses (

`NegLoss`

). For each observation in`X`

,`predict`

assigns the label of the class yielding the largest negated average binary loss (or, equivalently, the smallest average binary loss).An array of positive-class scores (

`PBScore`

) for the observations classified by each binary learner.

## Examples

### Predict Class Labels

Create an incremental learning model by converting a traditionally trained ECOC model, and predict class labels using both models.

Load the human activity data set.

`load humanactivity`

For details on the data set, enter `Description`

at the command line.

Fit a multiclass ECOC classification model to the entire data set.

Mdl = fitcecoc(feat,actid);

`Mdl`

is a `ClassificationECOC`

model object representing a traditionally trained ECOC classification model.

Convert the traditionally trained ECOC classification model to a model for incremental learning.

IncrementalMdl = incrementalLearner(Mdl)

IncrementalMdl = incrementalClassificationECOC IsWarm: 1 Metrics: [1x2 table] ClassNames: [1 2 3 4 5] ScoreTransform: 'none' BinaryLearners: {10x1 cell} CodingName: 'onevsone' Decoding: 'lossweighted'

`IncrementalMdl`

is an `incrementalClassificationECOC`

model object prepared for incremental learning.

The `incrementalLearner`

function initializes the incremental learner by passing the coding design and model parameters for binary learners to it, along with other information `Mdl`

extracts from the training data. `IncrementalMdl`

is warm (`IsWarm`

is `1`

), which means that incremental learning functions can track performance metrics and make predictions.

An incremental learner created from converting a traditionally trained model can generate predictions without further processing.

Predict class labels for all observations using both models.

ttlabels = predict(Mdl,feat); illables = predict(IncrementalMdl,feat); isequal(ttlabels,illables)

`ans = `*logical*
1

Both models predict the same labels for each observation.

### Compute Negated Average Binary Losses

Prepare an incremental ECOC model for `predict`

by fitting the model to a chunk of observations. Compute negated average binary losses for streaming data by using the `predict`

function, and evaluate the model performance using the area under the receiver operating characteristic (ROC) curve, or AUC.

Load the human activity data set. Randomly shuffle the data.

load humanactivity n = numel(actid); rng(10) % For reproducibility idx = randsample(n,n); X = feat(idx,:); Y = actid(idx);

For details on the data set, enter `Description`

at the command line.

Create an ECOC model for incremental learning. Specify the class names. Prepare the model for `predict`

by fitting the model to the first 10 observations.

Mdl = incrementalClassificationECOC(ClassNames=unique(Y)); initobs = 10; Mdl = fit(Mdl,X(1:initobs,:),Y(1:initobs));

`Mdl`

is an `incrementalClassificationECOC`

model. All its properties are read-only. The model is configured to generate predictions.

Simulate a data stream, and perform the following actions on each incoming chunk of 100 observations.

Call

`predict`

to compute negated average binary losses for each observation in the incoming chunk of data. Specify to use the`"lossbased"`

decoding scheme.Call

`rocmetrics`

to compute the AUC using the negated average binary losses, and store the AUC value, averaged over all classes. This AUC is an incremental measure of how well the model predicts the activities on average.Call

`fit`

to fit the model to the incoming chunk. Overwrite the previous incremental model with a new one fitted to the incoming observations.

numObsPerChunk = 100; nchunk = floor((n - initobs)/numObsPerChunk); auc = zeros(nchunk,1); % Incremental learning for j = 1:nchunk ibegin = min(n,numObsPerChunk*(j-1) + 1 + initobs); iend = min(n,numObsPerChunk*j + initobs); idx = ibegin:iend; [~,NegLoss] = predict(Mdl,X(idx,:),Decoding="lossbased"); mdlROC = rocmetrics(Y(idx),NegLoss,Mdl.ClassNames); [~,~,~,auc(j)] = average(mdlROC,"micro"); Mdl = fit(Mdl,X(idx,:),Y(idx)); end

`Mdl`

is an `incrementalClassificationECOC`

model object trained on all the data in the stream.

Plot the AUC values for each incoming chunk of data.

plot(auc) xlim([0 nchunk]) ylabel("AUC") xlabel("Iteration")

The plot suggests that the classifier predicts the activities well during incremental learning.

## Input Arguments

`Mdl`

— ECOC classification model for incremental learning

`incrementalClassificationECOC`

model object

ECOC classification model for incremental learning, specified as an `incrementalClassificationECOC`

model object. You can create
`Mdl`

by calling
`incrementalClassificationECOC`

directly, or by converting a
supported, traditionally trained machine learning model using the `incrementalLearner`

function.

You must configure `Mdl`

to predict labels for a batch of observations.

If

`Mdl`

is a converted, traditionally trained model, you can predict labels without any modifications.Otherwise, you must fit

`Mdl`

to data using`fit`

or`updateMetricsAndFit`

.

`X`

— Batch of predictor data

floating-point matrix

Batch of predictor data, specified as a floating-point matrix of
*n* observations and `Mdl.NumPredictors`

predictor
variables. The value of the `ObservationsIn`

name-value
argument determines the orientation of the variables and observations. The default
`ObservationsIn`

value is `"rows"`

, which indicates that
observations in the predictor data are oriented along the rows of
`X`

.

**Note**

`predict`

supports only floating-point
input predictor data. If your input data includes categorical data, you must prepare an encoded
version of the categorical data. Use `dummyvar`

to convert each categorical variable
to a numeric matrix of dummy variables. Then, concatenate all dummy variable matrices and any
other numeric predictors. For more details, see Dummy Variables.

**Data Types: **`single`

| `double`

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

**Example: **`BinaryLoss="quadratic",Decoding="lossbased"`

specifies the
quadratic binary learner loss function and the loss-based decoding scheme for aggregating
the binary losses.

`BinaryLoss`

— Binary learner loss function

`Mdl.BinaryLoss`

(default) | `"hamming"`

| `"linear"`

| `"logit"`

| `"exponential"`

| `"binodeviance"`

| `"hinge"`

| `"quadratic"`

| function handle

Binary learner loss function, specified as a built-in loss function name or function handle.

This table describes the built-in functions, where

*y*is the class label for a particular binary learner (in the set {–1,1,0}),_{j}*s*is the score for observation_{j}*j*, and*g*(*y*,_{j}*s*) is the binary loss formula._{j}Value Description Score Domain *g*(*y*,_{j}*s*)_{j}`"binodeviance"`

Binomial deviance (–∞,∞) log[1 + exp(–2 *y*)]/[2log(2)]_{j}s_{j}`"exponential"`

Exponential (–∞,∞) exp(– *y*)/2_{j}s_{j}`"hamming"`

Hamming [0,1] or (–∞,∞) [1 – sign( *y*)]/2_{j}s_{j}`"hinge"`

Hinge (–∞,∞) max(0,1 – *y*)/2_{j}s_{j}`"linear"`

Linear (–∞,∞) (1 – *y*)/2_{j}s_{j}`"logit"`

Logistic (–∞,∞) log[1 + exp(– *y*)]/[2log(2)]_{j}s_{j}`"quadratic"`

Quadratic [0,1] [1 – *y*(2_{j}*s*– 1)]_{j}^{2}/2The software normalizes binary losses so that the loss is 0.5 when

*y*= 0. Also, the software calculates the mean binary loss for each class [1]._{j}For a custom binary loss function, for example

`customFunction`

, specify its function handle`BinaryLoss=@customFunction`

.`customFunction`

has this form:bLoss = customFunction(M,s)

`M`

is the*K*-by-*B*coding matrix stored in`Mdl.CodingMatrix`

.`s`

is the 1-by-*B*row vector of classification scores.`bLoss`

is the classification loss. This scalar aggregates the binary losses for every learner in a particular class. For example, you can use the mean binary loss to aggregate the loss over the learners for each class.*K*is the number of classes.*B*is the number of binary learners.

For an example of a custom binary loss function, see Predict Test-Sample Labels of ECOC Model Using Custom Binary Loss Function. This example is for a traditionally trained model. You can define a custom loss function for incremental learning as shown in the example.

For more information, see Binary Loss.

**Data Types: **`char`

| `string`

| `function_handle`

`Decoding`

— Decoding scheme

`Mdl.Decoding`

(default) | `"lossweighted"`

| `"lossbased"`

Decoding scheme, specified as `"lossweighted"`

or
`"lossbased"`

.

The decoding scheme of an ECOC model specifies how the software aggregates the binary losses and determines the predicted class for each observation. The software supports two decoding schemes:

`"lossweighted"`

— The predicted class of an observation corresponds to the class that produces the minimum sum of the binary losses over binary learners.`"lossbased"`

— The predicted class of an observation corresponds to the class that produces the minimum average of the binary losses over binary learners.

For more information, see Binary Loss.

**Example: **`Decoding="lossbased"`

**Data Types: **`char`

| `string`

`ObservationsIn`

— Predictor data observation dimension

`"rows"`

(default) | `"columns"`

Predictor data observation dimension, specified as `"rows"`

or
`"columns"`

.

**Example: **`ObservationsIn="columns"`

**Data Types: **`char`

| `string`

## Output Arguments

`label`

— Predicted responses (labels)

categorical array | floating-point vector | character array | logical vector | string vector | cell array of character vectors

Predicted responses (labels), returned as a categorical or character array;
floating-point, logical, or string vector; or cell array of character vectors with
*n* rows. *n* is the number of observations in
`X`

, and `label(`

is
the predicted response for observation * j*)

`j`

. `label`

has the same data type as the class names stored in
`Mdl.ClassNames`

. (The software treats string arrays as cell arrays of character
vectors.)

The `predict`

function predicts the
classification of an observation by assigning the observation to the class yielding the largest
negated average binary loss (or, equivalently, the smallest average binary loss). For an
observation with `NaN`

loss values, the function classifies the observation
into the majority class, which makes up the largest proportion of the training labels.

`NegLoss`

— Negated average binary losses

numeric matrix

Negated average binary losses, returned as an
*n*-by-*K* numeric matrix. *n* is
the number of observations in `X`

, and *K* is the
number of distinct classes in the training data
(`numel(Mdl.ClassNames)`

).

`NegLoss(i,k)`

is the negated average binary loss for classifying observation
*i* into the *k*th class.

If

`Decoding`

is`'lossbased'`

, then`NegLoss(i,k)`

is the negated sum of the binary losses divided by the total number of binary learners.If

`Decoding`

is`'lossweighted'`

, then`NegLoss(i,k)`

is the negated sum of the binary losses divided by the number of binary learners for the*k*th class.

For more details, see Binary Loss.

`PBScore`

— Positive-class scores

numeric matrix

Positive-class scores for each binary learner, returned as an
*n*-by-*B* numeric matrix. *n* is
the number of observations in `X`

, and *B* is the
number of binary learners (`numel(Mdl.BinaryLearners)`

).

## More About

### Binary Loss

The *binary loss* is a function of the class and classification score that determines how well a binary learner classifies an observation into the class. The *decoding scheme* of an ECOC model specifies how the software aggregates the binary losses and determines the predicted class for each observation.

Assume the following:

*m*is element (_{kj}*k*,*j*) of the coding design matrix*M*—that is, the code corresponding to class*k*of binary learner*j*.*M*is a*K*-by-*B*matrix, where*K*is the number of classes, and*B*is the number of binary learners.*s*is the score of binary learner_{j}*j*for an observation.*g*is the binary loss function.$$\widehat{k}$$ is the predicted class for the observation.

The software supports two decoding schemes:

*Loss-based decoding*[2] (`Decoding`

is`'lossbased'`

) — The predicted class of an observation corresponds to the class that produces the minimum average of the binary losses over all binary learners.$$\widehat{k}=\underset{k}{\text{argmin}}\frac{1}{B}{\displaystyle \sum _{j=1}^{B}\left|{m}_{kj}\right|g}({m}_{kj},{s}_{j}).$$

*Loss-weighted decoding*[3] (`Decoding`

is`'lossweighted'`

) — The predicted class of an observation corresponds to the class that produces the minimum average of the binary losses over the binary learners for the corresponding class.$$\widehat{k}=\underset{k}{\text{argmin}}\frac{{\displaystyle \sum _{j=1}^{B}\left|{m}_{kj}\right|g}({m}_{kj},{s}_{j})}{{\displaystyle \sum}_{j=1}^{B}\left|{m}_{kj}\right|}.$$

The denominator corresponds to the number of binary learners for class

*k*. [1] suggests that loss-weighted decoding improves classification accuracy by keeping loss values for all classes in the same dynamic range.

The `predict`

, `resubPredict`

, and
`kfoldPredict`

functions return the negated value of the objective
function of `argmin`

as the second output argument
(`NegLoss`

) for each observation and class.

This table summarizes the supported binary loss functions, where
*y _{j}* is a class label for a particular
binary learner (in the set {–1,1,0}),

*s*is the score for observation

_{j}*j*, and

*g*(

*y*,

_{j}*s*) is the binary loss function.

_{j}Value | Description | Score Domain | g(y,_{j}s)_{j} |
---|---|---|---|

`"binodeviance"` | Binomial deviance | (–∞,∞) | log[1 +
exp(–2y)]/[2log(2)]_{j}s_{j} |

`"exponential"` | Exponential | (–∞,∞) | exp(–y)/2_{j}s_{j} |

`"hamming"` | Hamming | [0,1] or (–∞,∞) | [1 – sign(y)]/2_{j}s_{j} |

`"hinge"` | Hinge | (–∞,∞) | max(0,1 – y)/2_{j}s_{j} |

`"linear"` | Linear | (–∞,∞) | (1 – y)/2_{j}s_{j} |

`"logit"` | Logistic | (–∞,∞) | log[1 +
exp(–y)]/[2log(2)]_{j}s_{j} |

`"quadratic"` | Quadratic | [0,1] | [1 – y(2_{j}s –
1)]_{j}^{2}/2 |

The software normalizes binary losses so that the loss is 0.5 when
*y _{j}* = 0, and aggregates using the average
of the binary learners [1].

Do not confuse the binary loss with the overall classification loss (specified by the
`LossFun`

name-value argument of the `loss`

and
`predict`

object functions), which measures how well an ECOC classifier
performs as a whole.

## Algorithms

### Observation Weights

If the prior class probability distribution is known (in other words, the prior distribution is not empirical), `predict`

normalizes observation weights to sum to the prior class probabilities in the respective classes. This action implies that the default observation weights are the respective prior class probabilities.

If the prior class probability distribution is empirical, the software normalizes the specified observation weights to sum to 1 each time you call `predict`

.

## References

[1] Allwein, E., R. Schapire, and Y. Singer. “Reducing multiclass to binary: A unifying approach for margin classiﬁers.” *Journal of Machine Learning Research*. Vol. 1, 2000, pp. 113–141.

[2] Escalera, S., O. Pujol, and P. Radeva. “Separability of ternary codes for sparse designs of error-correcting output codes.” *Pattern Recog. Lett.*, Vol. 30, Issue 3, 2009, pp. 285–297.

[3] Escalera, S., O. Pujol, and P. Radeva. “On the decoding process in ternary error-correcting output codes.” *IEEE Transactions on Pattern Analysis and Machine Intelligence*. Vol. 32, Issue 7, 2010, pp. 120–134.

## Version History

**Introduced in R2022a**

## See Also

### Functions

### Objects

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