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Class Definition: CompactRegressionGP

statistics: CompactRegressionGP

Compact Gaussian process regression

A CompactRegressionGP object holds a Gaussian process regression model without its training data, keeping what is needed to predict and dropping the rest.

Create a CompactRegressionGP object by using the compact method of a RegressionGP object.

A compact model keeps the active set it predicts from, the prediction weights, the covariance function and its parameters, the explicit basis and its coefficients, the noise standard deviation and the standardizing location and scale. It drops the response, the observation weights, the rows used, the count of observations and the maximized log likelihood, so it can predict but cannot be cross validated, refitted, or asked for its resubstitution loss or its post-fit statistics.

The standard deviation and the prediction intervals remain available, because the active set of an exactly fitted model is the whole of the training predictors and the factorization can be rebuilt from it.

See also: RegressionGP, fitrgp

Source Code: CompactRegressionGP

The CompactRegressionGP class contains the following properties:

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

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

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

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A character vector. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A vector of positive integers, or empty. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

'Exact' or 'None'. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A character vector or a function handle. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A numeric vector, empty when the basis is 'None'. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A positive scalar. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A character vector or a function handle. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A structure with fields Name, KernelParameters and KernelParameterNames. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

'Exact'. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A numeric vector with one weight per active set vector. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

An MxP numeric matrix, standardized where the model standardized its predictors. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

'Random'. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A positive integer scalar. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A 1xP numeric vector, or empty. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A 1xP numeric vector, or empty. This property is read-only.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

A character vector, or the text of the function handle that was supplied. Assigning to it accepts either.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

The CompactRegressionGP class offers the following public methods:

CompactRegressionGP: obj = CompactRegressionGP (Mdl)

Mdl is the RegressionGP object to compact, and is required: the compact model has no training data to build itself from. The documented way to reach this constructor is the compact method.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03
CompactRegressionGP: yFit = predict (obj, XC)
CompactRegressionGP: [yFit, ySD, yInt] = predict (obj, XC)
CompactRegressionGP: […] = predict (…, 'Alpha', alpha)

yFit = predict (obj, XC) returns the predicted response of the CompactRegressionGP model obj at the points in XC, and the further outputs are the standard deviation of each predicted response and the prediction intervals, exactly as the full model returns them.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03
CompactRegressionGP: L = loss (obj, X, Y)
CompactRegressionGP: L = loss (…, name, value)

L = loss (obj, X, Y) returns the mean squared error of the model obj on the data X and Y, and accepts the same 'LossFun' and 'Weights' pairs the full model accepts.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03
CompactRegressionGP: savemodel (obj, filename)

savemodel (obj, filename) saves the model obj into filename in a form loadmodel can read back.

A compact model predicts what the full model predicts, and carries none of the training data.

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03

Examples 

 x = linspace (0, 1, 20)';
 y = sin (2*pi*x) + 0.05 * cos (9*x);
 Mdl = fitrgp (x, y);
 CMdl = compact (Mdl)
CMdl =

  CompactRegressionGP

             ResponseName: 'Y'
            NumPredictors: 1
           KernelFunction: 'SquaredExponential'
            PredictMethod: 'Exact'
                    Sigma: 0.00687107
 xq = [0.15; 0.55; 0.85];
 [yq, ysd] = predict (CMdl, xq)
yq =

   0.8193
  -0.2981
  -0.7981

ysd =

   7.8751e-03
   7.6921e-03
   7.8751e-03