Gaussian Process Regression

Gaussian process regression models (kriging)

Gaussian process regression (GPR) models are nonparametric, kernel-based probabilistic models. To train a GPR model interactively, use the Regression Learner app. For greater flexibility, train a GPR model using the fitrgp function at the command line. After training, you can predict responses for new data by passing the model and the new predictor data to the predict object function.

Apps

Regression Learner

Train regression models to predict data using supervised machine learning

Blocks

RegressionGP Predict

Predict responses using Gaussian process (GP) regression model (Since R2022a)

Functions

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Create Gaussian Process Regression Model or Template

`fitrgp`	Fit a Gaussian process regression (GPR) model
`compact`	Reduce size of machine learning model
`templateGP`	Gaussian process template (Since R2023b)

Interpret Prediction

`lime`	Local interpretable model-agnostic explanations (LIME) (Since R2020b)
`partialDependence`	Compute partial dependence (Since R2020b)
`permutationImportance`	Predictor importance by permutation (Since R2024a)
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`shapley`	Shapley values (Since R2021a)

Cross-Validate

`crossval`	Cross-validate machine learning model
`kfoldLoss`	Loss for cross-validated partitioned regression model
`kfoldPredict`	Predict responses for observations in cross-validated regression model
`kfoldfun`	Cross-validate function for regression

Measure Performance

`loss`	Regression error for Gaussian process regression model
`resubLoss`	Resubstitution regression loss
`postFitStatistics`	Compute post-fit statistics for the exact Gaussian process regression model

Predict Responses

`predict`	Predict response of Gaussian process regression model
`resubPredict`	Predict responses for training data using trained regression model

Use Regression Chains for Multiresponse Regression

`fitrchains`	Multiresponse regression with regression chains (Since R2024b)
`compact`	Reduce size of multiresponse regression model (Since R2024b)
`loss`	Loss for multiresponse regression model (Since R2024b)
`predict`	Predict responses using multiresponse regression model (Since R2024b)

Objects

`RegressionGP`	Gaussian process regression model
`CompactRegressionGP`	Compact Gaussian process regression model class
`RegressionPartitionedGP`	Cross-validated Gaussian process regression (GPR) model (Since R2022b)
`RegressionChainEnsemble`	Multiresponse regression model (Since R2024b)
`CompactRegressionChainEnsemble`	Compact multiresponse regression model (Since R2024b)

Topics

Gaussian Process Regression Models
Gaussian process regression (GPR) models are nonparametric kernel-based probabilistic models.
Kernel (Covariance) Function Options
In Gaussian processes, the covariance function expresses the expectation that points with similar predictor values will have similar response values.
Exact GPR Method
Learn the parameter estimation and prediction in exact GPR method.
Subset of Data Approximation for GPR Models
With large data sets, the subset of data approximation method can greatly reduce the time required to train a Gaussian process regression model.
Subset of Regressors Approximation for GPR Models
The subset of regressors approximation method replaces the exact kernel function by an approximation.
Fully Independent Conditional Approximation for GPR Models
The fully independent conditional (FIC) approximation is a way of systematically approximating the true GPR kernel function in a way that avoids the predictive variance problem of the SR approximation while still maintaining a valid Gaussian process.
Block Coordinate Descent Approximation for GPR Models
Block coordinate descent approximation is another approximation method used to reduce computation time with large data sets.
Predict Responses Using RegressionGP Predict Block
Train a Gaussian process (GP) regression model, and then use the RegressionGP Predict block for response prediction.

Featured Examples

Predict Battery State of Charge Using Machine Learning

Train a Gaussian process regression model to predict the state of charge of a battery in automotive engineering.

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