RegressionPartitionedKernel

Cross-validated kernel model for regression

Description

RegressionPartitionedKernel is a set of kernel regression models trained on cross-validated folds. To obtain a cross-validated, kernel regression model, use fitrkernel and specify one of the cross-validation options. You can estimate the predictive quality of the model, or how well the linear regression model generalizes, using one or more of these “kfold” methods: kfoldPredict and kfoldLoss.

Every “kfold” method uses models trained on training-fold observations to predict the response for validation-fold observations. For example, suppose that you cross-validate using five folds. In this case, the software randomly assigns each observation into five groups of equal size (roughly). The training fold contains four of the groups (that is, roughly 4/5 of the data) and the validation fold contains the other group (that is, roughly 1/5 of the data). In this case, cross-validation proceeds as follows:

1. The software trains the first model (stored in CVMdl.Trained{1}) using the observations in the last four groups and reserves the observations in the first group for validation.

2. The software trains the second model (stored in CVMdl.Trained{2}) using the observations in the first group and the last three groups. The software reserves the observations in the second group for validation.

3. The software proceeds in a similar fashion for the third through the fifth models.

If you validate by calling kfoldPredict, it computes predictions for the observations in group 1 using the first model, group 2 for the second model, and so on. In short, the software estimates a response for every observation using the model trained without that observation.

Note

RegressionPartitionedKernel model objects do not store the predictor data set.

Creation

Create a RegressionPartitionedKernel object using the fitrkernel function. Use one of the 'CrossVal', 'CVPartition', 'Holdout', 'KFold', or 'Leaveout' name-value pair arguments in the call to fitrkernel. For details, see the fitrkernel function reference page.

Properties

Cross-Validation Properties

CrossValidatedModel — Cross-validated model name

character vector

This property is read-only.

Cross-validated model name, specified as a character vector.

For example, 'Kernel' specifies a cross-validated kernel model.

Data Types: char

KFold — Number of cross-validated folds

positive integer scalar

This property is read-only.

Number of cross-validated folds, specified as a positive integer scalar.

Data Types: double

ModelParameters — Cross-validation parameter values

object

This property is read-only.

Cross-validation parameter values, specified as an object. The parameter values correspond to the name-value pair argument values used to cross-validate the kernel regression model. ModelParameters does not contain estimated parameters.

NumObservations — Number of observations

positive numeric scalar

This property is read-only.

Number of observations in the training data, specified as a positive numeric scalar.

Data Types: double

Partition — Data partition

cvpartition model

This property is read-only.

Data partition indicating how the software splits the data into cross-validation folds, specified as a cvpartition model.

Trained — Kernel regression models trained on cross-validation folds

cell array of RegressionKernel models

This property is read-only.

Kernel regression models trained on cross-validation folds, specified as a cell array of RegressionKernel models. Trained has k cells, where k is the number of folds.

Data Types: cell

W — Observation weights

numeric vector

This property is read-only.

Observation weights used to cross-validate the model, specified as a numeric vector. W has NumObservations elements.

The software normalizes the weights used for training so that sum(W,'omitnan') is 1.

Data Types: single | double

Y — Observed response values

numeric vector

This property is read-only.

Observed response values used to cross-validate the model, specified as a numeric vector. Y has NumObservations elements.

Each row of Y represents the observed response of the corresponding observation in the predictor data.

Data Types: single | double

Other Regression Properties

CategoricalPredictors — Categorical predictor indices

vector of positive integers | []

This property is read-only.

Categorical predictor indices, specified as a vector of positive integers. CategoricalPredictors contains index values indicating that the corresponding predictors are categorical. The index values are between 1 and p, where p is the number of predictors used to train the model. If none of the predictors are categorical, then this property is empty ([]).

Data Types: single | double

PredictorNames — Predictor names

cell array of character vectors

This property is read-only.

Predictor names in order of their appearance in the predictor data, specified as a cell array of character vectors. The length of PredictorNames is equal to the number of columns used as predictor variables in the training data X or Tbl.

Data Types: cell

ResponseName — Response variable name

character vector

This property is read-only.

Response variable name, specified as a character vector.

Data Types: char

ResponseTransform — Response transformation function

'none' | function handle

Response transformation function, specified as 'none' or a function handle. ResponseTransform describes how the software transforms raw response values predicted by the model.

For a MATLAB^® function, or a function that you define, enter its function handle. For example, you can enter Mdl.ResponseTransform = @function, where function accepts a numeric vector of the original responses and returns a numeric vector of the same size containing the transformed responses.

Data Types: char | string | function_handle

Object Functions

kfoldLoss	Regression loss for cross-validated kernel regression model
kfoldPredict	Predict responses for observations in cross-validated kernel regression model

Examples

Create Cross-Validated Kernel Regression Model

Simulate sample data.

rng(0,'twister'); % For reproducibility
n = 1000;
x = linspace(-10,10,n)';
y = 1 + x*2e-2 + sin(x)./x + 0.2*randn(n,1);

Cross-validate a kernel regression model.

CVMdl = fitrkernel(x,y,'Kfold',5);

CVMdl is a RegressionPartitionedKernel 5-fold cross-validated model. CVMdl.Trained contains a cell vector of five RegressionKernel models. Display the trained property.

CVMdl.Trained

ans=5×1 cell array
    {1x1 RegressionKernel}
    {1x1 RegressionKernel}
    {1x1 RegressionKernel}
    {1x1 RegressionKernel}
    {1x1 RegressionKernel}

Each cell contains a kernel regression model trained on four folds, then tested on the remaining fold.

Predict responses for observations in the validation folds and estimate the generalization error by passing CVMdl to kfoldPredict and kfoldLoss, respectively.

yHat = kfoldPredict(CVMdl);
L = kfoldLoss(CVMdl)

L = 
0.0406

kfoldLoss computes the average mean squared error for all the folds by default. The estimated mean squared error is 0.1887.

Version History

Introduced in R2018b