kfoldPredict

Predict responses for observations in cross-validated linear regression model

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Syntax

YHat = kfoldPredict(CVMdl)
YHat = kfoldPredict(CVMdl,PredictionForMissingValue=prediction)

Description

YHat = kfoldPredict(CVMdl) returns cross-validated predicted responses by the cross-validated linear regression model CVMdl. For every fold, kfoldPredict predicts the responses for validation-fold observations using a model trained on training-fold observations.

YHat contains predicted responses for each regularization strength in the linear regression models that compose CVMdl.

example

YHat = kfoldPredict(CVMdl,PredictionForMissingValue=prediction) uses the prediction value as the predicted response for observations with missing values in the predictor data. By default, kfoldPredict uses the median of the observed response values in the training-fold data. (since R2023b)

Examples

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Open Live Script

Simulate 10000 observations from this model

y=x100+2x200+e.

  • X=x1,...,x1000 is a 10000-by-1000 sparse matrix with 10% nonzero standard normal elements.

  • e is random normal error with mean 0 and standard deviation 0.3.

rng(1) % For reproducibility
n = 1e4;
d = 1e3;
nz = 0.1;
X = sprandn(n,d,nz);
Y = X(:,100) + 2*X(:,200) + 0.3*randn(n,1);

Cross-validate a linear regression model. 

CVMdl = fitrlinear(X,Y,'CrossVal','on')
CVMdl = 
  RegressionPartitionedLinear
    CrossValidatedModel: 'Linear'
           ResponseName: 'Y'
        NumObservations: 10000
                  KFold: 10
              Partition: [1×1 cvpartition]
      ResponseTransform: 'none'


  Properties, Methods


Mdl1 = CVMdl.Trained{1}
Mdl1 = 
  RegressionLinear
         ResponseName: 'Y'
    ResponseTransform: 'none'
                 Beta: [1000×1 double]
                 Bias: 0.0107
               Lambda: 1.1111e-04
              Learner: 'svm'


  Properties, Methods

By default, fitrlinear implements 10-fold cross-validation. CVMdl is a RegressionPartitionedLinear model. It contains the property Trained, which is a 10-by-1 cell array holding 10 RegressionLinear models that the software trained using the training set.

Predict responses for observations that fitrlinear did not use in training the folds.

yHat = kfoldPredict(CVMdl);

Because there is one regularization strength in Mdl, yHat is a numeric vector.

Open Live Script

Simulate 10000 observations as in Predict Cross-Validated Responses.

rng(1) % For reproducibility
n = 1e4;
d = 1e3;
nz = 0.1;
X = sprandn(n,d,nz);
Y = X(:,100) + 2*X(:,200) + 0.3*randn(n,1);

Create a set of 15 logarithmically-spaced regularization strengths from 10-5 through 10-1.

Lambda = logspace(-5,-1,15);

Cross-validate the models. To increase execution speed, transpose the predictor data and specify that the observations are in columns. Specify using least squares with a lasso penalty and optimizing the objective function using SpaRSA.

X = X'; 
CVMdl = fitrlinear(X,Y,'ObservationsIn','columns','KFold',5,'Lambda',Lambda,...
    'Learner','leastsquares','Solver','sparsa','Regularization','lasso');

CVMdl is a RegressionPartitionedLinear model. Its Trained property contains a 5-by-1 cell array of trained RegressionLinear models, each one holds out a different fold during training. Because fitrlinear trained using 15 regularization strengths, you can think of each RegressionLinear model as 15 models.

Predict cross-validated responses.

YHat = kfoldPredict(CVMdl);
size(YHat)
ans = 1×2

       10000          15


YHat(2,:)
ans = 1×15

   -1.7338   -1.7332   -1.7319   -1.7299   -1.7266   -1.7239   -1.7135   -1.7210   -1.7324   -1.7063   -1.6397   -1.5112   -1.2631   -0.7841   -0.0096

YHat is a 10000-by-15 matrix. YHat(2,:) is the cross-validated response for observation 2 using the model regularized with all 15 regularization values.

Input Arguments

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Cross-validated, linear regression model, specified as a RegressionPartitionedLinear model object. You can create a RegressionPartitionedLinear model using fitrlinear and specifying any of the one of the cross-validation, name-value pair arguments, for example, CrossVal.

To obtain estimates, kfoldPredict applies the same data used to cross-validate the linear regression model (X and Y).

Since R2023b

Predicted response value to use for observations with missing predictor values, specified as "median", "mean", or a numeric scalar.

ValueDescription
"median"kfoldPredict uses the median of the observed response values in the training-fold data as the predicted response value for observations with missing predictor values.
"mean"kfoldPredict uses the mean of the observed response values in the training-fold data as the predicted response value for observations with missing predictor values.
Numeric scalarkfoldPredict uses this value as the predicted response value for observations with missing predictor values.

Example: "mean"

Example: NaN

Data Types: single | double | char | string

Output Arguments

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Cross-validated predicted responses, returned as an n-by-L numeric array. n is the number of observations in the predictor data that created CVMdl (see X) and L is the number of regularization strengths in CVMdl.Trained{1}.Lambda. YHat(i,j) is the predicted response for observation i using the linear regression model that has regularization strength CVMdl.Trained{1}.Lambda(j).

The predicted response using the model with regularization strength j is y^j=xβj+bj.

  • x is an observation from the predictor data matrix X, and is row vector.

  • βj is the estimated column vector of coefficients. The software stores this vector in Mdl.Beta(:,j).

  • bj is the estimated, scalar bias, which the software stores in Mdl.Bias(j).

Extended Capabilities

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Version History

Introduced in R2016a

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See Also

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