Modellerstellung und -Bewertung

Synthetische Datengenerierung, Merkmalsauswahl, Merkmalsentwicklung, Modellauswahl, Hyperparameter-Optimierung, Kreuzvalidierung, Rückstandsdiagnose und Diagramme

Wenn Sie ein hochwertiges Regressionsmodell erstellen, ist es wichtig, die richtigen Merkmale (oder Prädiktoren) auszuwählen, Hyperparameter (Modellparameter, die nicht an die Daten angepasst sind) abzustimmen und die Modellannahmen durch Rückstandsdiagnose zu bewerten. Sie können Hyperparameter abstimmen, indem Sie iterativ Werte für diese Parameter wählen und ein Modell mit diesen Einstellungen kreuzvalidieren. Dieser Prozess ergibt mehrere Modelle; das beste dieser Modelle könnte das sein, das den geschätzten Generalisierungsfehler minimiert.

Sie können die folgenden Aktionen durchführen, um Regressionsmodelle zu erstellen und zu bewerten:

Vor dem Training eines Regressionsmodells mithilfe von synthesizeTabularData, binningTabularSynthesizer oder smoteTabularSynthesizer synthetische Daten aus einem bestehenden Datensatz generieren.
Vor dem Training eines Regressionsmodells mithilfe von genrfeatures neue Merkmale entwickeln.
Regressionsmodelle interaktiv mithilfe der Regression Learner App erstellen und bewerten.
Mithilfe von fitrauto automatisch ein Modell mit abgestimmten Hyperparametern auswählen. Die Funktion probiert eine Auswahl an Regressionsmodelltypen mit verschiedenen Hyperparameterwerten aus und gibt ein finales Modell zurück, das eine gute Leistung aufweisen sollte. Verwenden Sie fitrauto, wenn Sie sich nicht sicher sind, welche Regressionsmodelltypen am besten zu Ihren Daten passen.
Hyperparameter eines bestimmten Modells abstimmen, indem Sie die Hyperparameterwerte auswählen und das Modell mit diesen Werten kreuzvalidieren. Um ein SVM-Modell abzustimmen, wählen Sie beispielsweise einen Satz Box-Randbedingungen und Kernel-Skalen, kreuzvalidieren ein Modell für jedes Wertepaar und vergleichen daraufhin die 10-fachen kreuzvalidierten mittleren quadratischen Fehlerschätzungen. Bestimmte nichtparametrische Regressionsfunktionen in Statistics and Machine Learning Toolbox™ bieten eine automatische Hyperparameter-Abstimmung über bayessche Optimierung, Rastersuche oder zufällige Suche. bayesopt, die Hauptfunktion zur Implementierung einer bayesschen Optimierung, ist zudem flexibel genug für viele andere Anwendungen. Weitere Informationen finden Sie unter Bayesian Optimization Workflow.
Mithilfe von lime, shapley und plotPartialDependence können Sie ein Regressionsmodell auswerten.
Mithilfe von sliceMetrics können Sie die Leistung eines Regressionsmodells bei separaten Datenslices auswerten.

Apps

Regression Learner

Train regression models to predict data using supervised machine learning

Funktionen

alle erweitern

Datensynthese

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

Merkmalsauswahl

`fsrftest`	Univariate feature ranking for regression using F-tests
`fsrmrmr`	Rank features for regression using minimum redundancy maximum relevance (MRMR) algorithm (Seit 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 (Seit 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 (Seit R2023b)
`sequentialfs`	Sequential feature selection using custom criterion
`stepwiselm`	Perform stepwise regression
`stepwiseglm`	Create generalized linear regression model by stepwise regression

Merkmalsentwicklung

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

Automatische Modellauswahl

fitrauto Automatically select regression model with optimized hyperparameters

Hyperparameter-Optimierung

`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 (Seit R2024b)
`plot`	Plot aggregated hyperparameter optimization results (Seit R2024b)
`resume`	Resume hyperparameter optimization problems (Seit R2024b)
`summary`	Summary table for `AggregateBayesianOptimization` object (Seit R2024b)

Kreuzvalidierung

Für zeitunabhängige Daten

`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 (Seit R2025a)
`test`	Test indices for cross-validation
`training`	Training indices for cross-validation

Für Zeitreihendaten

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

Modellauswertung

Local Interpretable Model-Agnostic Explanations (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)

Shapley-Werte

`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) (Seit R2024a)
`plotDependence`	Plot dependence of Shapley values on predictor values (Seit R2024b)
`swarmchart`	Visualize Shapley values using swarm scatter charts (Seit R2024a)

Partielle Abhängigkeit

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

Datenslice-Metriken

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

Diagnostik linearer Modelle

`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

Diagnostik generalisierter linearer Modelle

`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

Diagnostik nichtlinearer Modelle

`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

Lineare Hypothesentests

linhyptest Linear hypothesis test

Objekte

alle erweitern

Merkmalsauswahl

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

Merkmalsentwicklung

FeatureTransformer Generated feature transformations

Hyperparameter-Optimierung

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

Themen

Workflow der Regression Learner App

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.

Merkmalsauswahl

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.

Merkmalsentwicklung

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.

Automatische Modellauswahl

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.

Hyperparameter-Optimierung

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.

Kreuzvalidierung

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.

Modellauswertung

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.

Unsicherheitsschätzung

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.

Diagnostik linearer Modelle

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.

Diagnostik generalisierter linearer Modelle

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

Diagnostik nichtlinearer Modelle

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