Costruzione e valutazione del modello

Generazione di dati sintetici, selezione delle feature, ingegneria delle feature, selezione dei modelli, ottimizzazione degli iperparametri, validazione incrociata, diagnostica dei residui e grafici

Quando si costruisce un modello di regressione di alta qualità, è importante selezionare le feature (o predittori) corretti, ottimizzare gli iperparametri (parametri del modello non adattati ai dati) e valutare le ipotesi del modello attraverso la diagnostica dei residui. È possibile ottimizzare gli iperparametri iterando tra la scelta dei loro valori ed eseguire la validazione incrociata di un modello utilizzando tali scelte. Questo processo produce diversi modelli e il migliore tra questi potrebbe essere quello che minimizza l'errore di generalizzazione stimato.

È possibile eseguire le seguenti operazioni per costruire e valutare i modelli di regressione:

Generare dati sintetici a partire da un insieme di dati esistente prima dell'addestramento di un modello di regressione utilizzando synthesizeTabularData, binningTabularSynthesizer o smoteTabularSynthesizer.
Progettare nuove feature prima dell'addestramento di un modello di regressione utilizzando genrfeatures.
Costruire e valutare i modelli di regressione in modo interattivo utilizzando l'app Regression Learner.
Selezionare automaticamente un modello con iperparametri ottimizzati utilizzando fitrauto. La funzione prova una selezione di tipi di modello di regressione con diversi valori di iperparametri e restituisce un modello finale che dovrebbe garantire buone prestazioni. Utilizzare fitrauto quando non si è sicuri di quale tipo di modello di regressione sia più adatto ai dati.
Ottimizzare gli iperparametri di un modello specifico selezionando i valori degli iperparametri ed eseguire la validazione incrociata del modello utilizzando tali valori. Ad esempio, per ottimizzare un modello SVM, scegliere un insieme di constraint box e scale del kernel, eseguire la validazione incrociata del modello per ciascuna coppia di valori, quindi confrontare le rispettive stime dell'errore quadratico medio ottenute tramite validazione incrociata a 10 partizioni. Alcune funzioni di regressione non parametrica in Statistics and Machine Learning Toolbox™ offrono l'ottimizzazione automatica degli iperparametri tramite ottimizzazione bayesiana, ricerca su griglia o ricerca casuale. bayesopt, la funzione principale per l'implementazione dell'ottimizzazione bayesiana, è sufficientemente flessibile da poter essere utilizzata anche in molte altre applicazioni. Per ulteriori dettagli, vedere Bayesian Optimization Workflow.
Interpretare un modello di regressione utilizzando lime, shapley e plotPartialDependence.
Valutare le prestazioni di un modello di regressione su sezioni distinte di dati utilizzando sliceMetrics.

App

Regression Learner

Train regression models to predict data using supervised machine learning

Funzioni

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Sintesi dei dati

`synthesizeTabularData`	Synthesize tabular data (Da R2024b)
`binningTabularSynthesizer`	Binning-based synthesizer for tabular data synthesis (Da R2024b)
`smoteTabularSynthesizer`	SMOTE-based synthesizer for tabular data synthesis (Da R2026a)
`synthesizeTabularData`	Synthesize tabular data using binning-based or SMOTE-based synthesizer (Da R2024b)
`mmdtest`	Two-sample multivariate hypothesis test using maximum mean discrepancy (MMD) (Da R2024b)
`knntest`	Two-sample multivariate hypothesis test using k-nearest neighbors (KNN) (Da R2025a)

Selezione delle feature

`fsrftest`	Univariate feature ranking for regression using F-tests
`fsrmrmr`	Rank features for regression using minimum redundancy maximum relevance (MRMR) algorithm (Da R2022a)
`fsrnca`	Feature selection using neighborhood component analysis for regression
`oobPermutedPredictorImportance`	Out-of-bag predictor importance estimates for random forest of regression trees by permutation
`partialDependence`	Compute partial dependence
`permutationImportance`	Predictor importance by permutation (Da R2024a)
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`predictorImportance`	Estimates of predictor importance for regression tree
`predictorImportance`	Estimates of predictor importance for regression ensemble of decision trees
`relieff`	Rank importance of predictors using ReliefF or RReliefF algorithm
`selectFeatures`	Select important features for NCA classification or regression (Da R2023b)
`sequentialfs`	Sequential feature selection using custom criterion
`stepwiselm`	Perform stepwise regression
`stepwiseglm`	Create generalized linear regression model by stepwise regression

Ingegneria delle feature

`genrfeatures`	Perform automated feature engineering for regression (Da R2021b)
`describe`	Describe generated features
`transform`	Transform new data using generated features

Selezione automatica dei modelli

fitrauto Automatically select regression model with optimized hyperparameters

Ottimizzazione degli iperparametri

`bayesopt`	Select optimal machine learning hyperparameters using Bayesian optimization
`hyperparameters`	Variable descriptions for optimizing a fit function
`optimizableVariable`	Variable description for `bayesopt` or other optimizers
`learnersize`	Compact size of trained machine learning model object (Da R2024b)
`plot`	Plot aggregated hyperparameter optimization results (Da R2024b)
`resume`	Resume hyperparameter optimization problems (Da R2024b)
`summary`	Summary table for `AggregateBayesianOptimization` object (Da R2024b)

Validazione incrociata

Per dati indipendenti dal tempo

`crossval`	Estimate loss using cross-validation
`cvpartition`	Partition data for cross-validation
`repartition`	Repartition data for cross-validation
`summary`	Summarize cross-validation partition with stratification or grouping variable (Da R2025a)
`test`	Test indices for cross-validation
`training`	Training indices for cross-validation

Per dati delle serie temporali

`tspartition`	Partition time series data for cross-validation (Da R2022b)
`test`	Test indices for time series cross-validation (Da R2022b)
`training`	Training indices for time series cross-validation (Da R2022b)

Interpretazione del modello

Spiegazioni locali interpretabili e indipendenti dal modello (LIME)

`lime`	Local interpretable model-agnostic explanations (LIME)
`fit`	Fit simple model of local interpretable model-agnostic explanations (LIME)
`plot`	Plot results of local interpretable model-agnostic explanations (LIME)

Valori di Shapley

`shapley`	Shapley values
`fit`	Compute Shapley values for query points
`plot`	Plot Shapley values using bar graphs
`boxchart`	Visualize Shapley values using box charts (box plots) (Da R2024a)
`plotDependence`	Plot dependence of Shapley values on predictor values (Da R2024b)
`swarmchart`	Visualize Shapley values using swarm scatter charts (Da R2024a)

Dipendenza parziale

`partialDependence`	Compute partial dependence
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots

Metriche relative alle sezioni di dati

`sliceMetrics`	Metrics on data slices for machine learning model (Da R2026a)
`plot`	Plot bar graph of slice metric (Da R2026a)
`report`	Generate slice metrics report (Da R2026a)

Diagnostica del modello lineare

`coefCI`	Confidence intervals of coefficient estimates of linear regression model
`coefTest`	Linear hypothesis test on linear regression model coefficients
`dwtest`	Durbin-Watson test with linear regression model object
`plot`	Scatter plot or added variable plot of linear regression model
`plotAdded`	Added variable plot of linear regression model
`plotAdjustedResponse`	Adjusted response plot of linear regression model
`plotDiagnostics`	Plot observation diagnostics of linear regression model
`plotEffects`	Plot main effects of predictors in linear regression model
`plotInteraction`	Plot interaction effects of two predictors in linear regression model
`plotResiduals`	Plot residuals of linear regression model
`plotSlice`	Plot of slices through fitted linear regression surface

Diagnostica del modello lineare generalizzato

`coefCI`	Confidence intervals of coefficient estimates of generalized linear regression model
`coefTest`	Linear hypothesis test on generalized linear regression model coefficients
`devianceTest`	Analysis of deviance for generalized linear regression model
`plotDiagnostics`	Plot observation diagnostics of generalized linear regression model
`plotResiduals`	Plot residuals of generalized linear regression model
`plotSlice`	Plot of slices through fitted generalized linear regression surface

Diagnostica del modello non lineare

`coefCI`	Confidence intervals of coefficient estimates of nonlinear regression model
`coefTest`	Linear hypothesis test on nonlinear regression model coefficients
`plotDiagnostics`	Plot diagnostics of nonlinear regression model
`plotSlice`	Plot of slices through fitted nonlinear regression surface

Test di ipotesi lineari

linhyptest Linear hypothesis test

Oggetti

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Selezione delle feature

FeatureSelectionNCARegression Feature selection for regression using neighborhood component analysis (NCA)

Ingegneria delle feature

FeatureTransformer Generated feature transformations

Ottimizzazione degli iperparametri

`BayesianOptimization`	Bayesian optimization results
`HyperparameterOptimizationOptions`	Hyperparameter optimization options (Da R2024b)
`AggregateBayesianOptimization`	Aggregate Bayesian optimization results (Da R2024b)
`SupervisedLearningBayesianOptimization`	Results of Bayesian optimization for supervised learning model (Da R2026a)

Argomenti

Workflow dell'app Regression Learner

Train Regression Models in Regression Learner App
Workflow for training, comparing and improving regression models, including automated, manual, and parallel training.
Choose Model Options In Regression Learner
In Regression Learner, automatically train a selection of models, or compare and tune options of linear regression models, regression trees, support vector machines, Gaussian process regression models, kernel approximation models, ensembles of regression trees, and regression neural networks.
Feature Selection and Feature Transformation Using Regression Learner App
Identify useful predictors using plots or feature ranking algorithms, select features to include, and transform features using PCA in Regression Learner.
Visualize and Assess Model Performance in Regression Learner
Compare model metrics and visualize results.

Selezione delle feature

Introduction to Feature Selection
Learn about feature selection algorithms and explore the functions available for feature selection.
Sequential Feature Selection
This topic introduces sequential feature selection and provides an example that selects features sequentially using a custom criterion and the sequentialfs function.
Neighborhood Component Analysis (NCA) Feature Selection
Neighborhood component analysis (NCA) is a non-parametric method for selecting features with the goal of maximizing prediction accuracy of regression and classification algorithms.
Robust Feature Selection Using NCA for Regression
Perform feature selection that is robust to outliers using a custom robust loss function in NCA.
Select Predictors for Random Forests
Select split-predictors for random forests using interaction test algorithm.

Ingegneria delle feature

Automated Feature Engineering for Regression
Use genrfeatures to engineer new features before training a regression model. Before making predictions on new data, apply the same feature transformations to the new data set.

Selezione automatica dei modelli

Automated Regression Model Selection with Bayesian and ASHA Optimization
Use fitrauto to automatically try a selection of regression model types with different hyperparameter values, given training predictor and response data.

Ottimizzazione degli iperparametri

Bayesian Optimization Workflow
Perform Bayesian optimization using a fit function or by calling bayesopt directly.
Variables for a Bayesian Optimization
Create variables for Bayesian optimization.
Bayesian Optimization Objective Functions
Create the objective function for Bayesian optimization.
Constraints in Bayesian Optimization
Set different types of constraints for Bayesian optimization.
Optimize a Boosted Regression Ensemble
Minimize cross-validation loss of a regression ensemble.
Bayesian Optimization Plot Functions
Visually monitor a Bayesian optimization.
Bayesian Optimization Output Functions
Monitor a Bayesian optimization.
Bayesian Optimization Algorithm
Understand the underlying algorithms for Bayesian optimization.
Bayesian Optimization with Tall Arrays
Perform Bayesian optimization to select optimal parameters for training a kernel classifier on tall arrays.
Parallel Bayesian Optimization
How Bayesian optimization works in parallel.

Validazione incrociata

Implement Cross-Validation Using Parallel Computing
Speed up cross-validation using parallel computing.
Perform Time Series Direct Forecasting with directforecaster
Perform time series direct forecasting with the directforecaster function.
Manually Perform Time Series Forecasting Using Ensembles of Boosted Regression Trees
Manually perform single-step and multiple-step time series forecasting with ensembles of boosted regression trees.

Interpretazione del modello

Interpret Machine Learning Models
Explain model predictions using the lime and shapley objects and the plotPartialDependence function.
Shapley Values for Machine Learning Model
Compute Shapley values for a machine learning model using interventional algorithm or conditional algorithm.
Shapley Output Functions
Stop Shapley computations, create plots, save information to your workspace, or perform calculations while using shapley.

Stima dell'incertezza

Uncertainty Estimation for Regression
Learn about estimating the uncertainty of the true response for a regression problem.
Create Prediction Intervals Using Split Conformal Prediction
Create a prediction interval and use conformalized quantile regression to calibrate the prediction interval.

Diagnostica del modello lineare

Interpret Linear Regression Results
Display and interpret linear regression output statistics.
Linear Regression
Fit a linear regression model and examine the result.
Linear Regression with Interaction Effects
Construct and analyze a linear regression model with interaction effects and interpret the results.
Summary of Output and Diagnostic Statistics
Evaluate a fitted model by using model properties and object functions.
F-statistic and t-statistic
In linear regression, the F-statistic is the test statistic for the analysis of variance (ANOVA) approach to test the significance of the model or the components in the model. The t-statistic is useful for making inferences about the regression coefficients.
Coefficient of Determination (R-Squared)
Coefficient of determination (R-squared) indicates the proportionate amount of variation in the response variable y explained by the independent variables X in the linear regression model.
Coefficient Standard Errors and Confidence Intervals
Estimated coefficient variances and covariances capture the precision of regression coefficient estimates.
Residuals
Residuals are useful for detecting outlying y values and checking the linear regression assumptions with respect to the error term in the regression model.
Durbin-Watson Test
The Durbin-Watson test assesses whether or not there is autocorrelation among the residuals of time series data.
Cook’s Distance
Cook's distance is useful for identifying outliers in the X values (observations for predictor variables).
Hat Matrix and Leverage
The hat matrix provides a measure of leverage.
Delete-1 Statistics
Delete-1 change in covariance (CovRatio) identifies the observations that are influential in the regression fit.

Diagnostica del modello lineare generalizzato

Generalized Linear Models
Generalized linear models use linear methods to describe a potentially nonlinear relationship between predictor terms and a response variable.

Diagnostica del modello non lineare

Nonlinear Regression
Parametric nonlinear models represent the relationship between a continuous response variable and one or more continuous predictor variables.