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Class Definition: RegressionPartitionedKernel

statistics: RegressionPartitionedKernel

Cross-validated Gaussian kernel regression model.

A RegressionPartitionedKernel object holds one RegressionKernel per fold of a partition, each fitted to the observations the fold trains on. kfoldPredict predicts each observation with the fold that held it out, so what it returns is an out-of-sample prediction.

A RegressionKernel stores no copy of its training data and so has no resubstitution methods and no compact form. This class is what takes their place: cross-validation is the way a kernel model is asked how it would do on data it has not seen.

Every fold draws its own random basis, as it must, being its own fit. Two folds therefore approximate the same kernel through different expansions, which is a source of variation between folds over and above the data they were given. A larger 'NumExpansionDimensions' narrows it.

Create one with fitrlinear and a cross-validation option, or directly.

See also: fitrlinear, RegressionKernel, RegressionPartitionedKernel

Source Code: RegressionPartitionedKernel

The RegressionPartitionedKernel class contains the following properties:

A character vector, or the text of the function handle that was supplied, which may be assigned after the model is built. The fold models carry no transform of their own; this one is applied once to the assembled predictions.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 64.938

Always 'Linear', the short name MATLAB uses. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 65.766

A positive integer scalar, counting the rows that survived the removal of missing values. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 64.637

An Nx1 numeric vector. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 71.217

An Nx1 numeric vector summing to one. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 65.854

A cell array of character vectors. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 68.702

A row vector of column indices, empty when every predictor is numeric. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 66.942

A character vector, defaulting to 'Y'. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 65.598

A cell column with one RegressionKernel per fold, each fitted to the observations its fold trains on. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 67.267

A positive integer scalar. A holdout partition has one fold and a leave-one-out partition has as many as there are observations. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 67.851

A cvpartition object over the retained observations. This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 73.863

A structure holding the parameters the folds were fitted with, carried through from the learner that was cross validated, beside NLearn, the number of folds, and the Version, Method and Type tags of this class, with LearnerTemplates naming the backing. The learner’s own tags are replaced rather than kept, so a cross-validated SVM reports Method as 'PartitionedKernel' and not 'SVM'.

Deviation from MATLAB. MATLAB reports the parameter record of the cross-validation ensemble here rather than of the learner, so it says nothing at all about how the folds were fitted: of its eighteen fields only the fold count, its partitioner and a fit template carry anything, and the rest are boosting settings left inert. Nor can the parameters be reached through the folds, a compact model carrying none in MATLAB. This class reports the fit instead, which is strictly more than MATLAB offers, and everything MATLAB’s record does carry is published here as the KFold, Partition, X, Y, W and CrossValidatedModel properties.

This property is read-only.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 64.890

The RegressionPartitionedKernel class offers the following public methods:

RegressionPartitionedKernel: obj = RegressionPartitionedKernel (X, Y)
RegressionPartitionedKernel: obj = RegressionPartitionedKernel (…, name, value)

obj = RegressionPartitionedKernel (X, Y) partitions the data into ten folds and fits a RegressionKernel to each.

obj = RegressionPartitionedKernel (…, name, value) takes one of 'KFold', 'Holdout', 'Leaveout' and 'CVPartition' to say how to partition, and any option RegressionKernel takes to say how to fit. 'CrossVal' is accepted and has no effect here, this class being cross-validated by construction.

Anything left as 'auto' is resolved by each fold against its own training rows rather than once over the whole data, so ten folds of a hundred observations each get a Lambda of one ninetieth rather than one hundredth, and each its own Epsilon and KernelScale. Both are MATLAB’s behaviour, measured.

See also: fitrlinear, RegressionKernel

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 65.811
RegressionPartitionedKernel: yFit = kfoldPredict (obj)

Each observation is predicted by the fold that held it out, so the predictions are out-of-sample. An observation that no fold held out, which under a holdout partition is most of them, comes back NaN.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 70.171
RegressionPartitionedKernel: l = kfoldLoss (obj)
RegressionPartitionedKernel: l = kfoldLoss (…, name, value)

l = kfoldLoss (obj) returns the out-of-fold mean squared error.

l = kfoldLoss (…, name, value) takes 'LossFun', either 'mse' or 'epsiloninsensitive'; 'Folds', a subset of the folds to average over; and 'Mode', either 'average', the default, or 'individual', which returns one row per fold.

Cross-validate a Gaussian kernel regression of fuel consumption and read the out-of-sample mean squared error.

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 66.470

Examples 

 load carsmall
 X = [Acceleration, Displacement, Horsepower, Weight];
 ok = ! any (isnan ([X, MPG]), 2);
 CVMdl = RegressionPartitionedKernel (X(ok,:), MPG(ok), 'KFold', 5)
CVMdl =

  RegressionPartitionedKernel

      CrossValidatedModel: 'Kernel'
             ResponseName: 'Y'
        ResponseTransform: 'none'
          NumObservations: 93
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 69.403