Predict responses for Gaussian kernel regression model



YFit = predict(Mdl,X) returns a vector of predicted responses for the predictor data in the matrix or table X, based on the binary Gaussian kernel regression model Mdl.


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Predict the test set responses using a Gaussian kernel regression model for the carbig data set.

Load the carbig data set.

load carbig

Specify the predictor variables (X) and the response variable (Y).

X = [Weight,Cylinders,Horsepower,Model_Year];
Y = MPG;

Delete rows of X and Y where either array has NaN values. Removing rows with NaN values before passing data to fitrkernel can speed up training and reduce memory usage.

R = rmmissing([X Y]); 
X = R(:,1:4); 
Y = R(:,end); 

Reserve 10% of the observations as a holdout sample. Extract the training and test indices from the partition definition.

rng(10)  % For reproducibility 
N = length(Y); 
cvp = cvpartition(N,'Holdout',0.1);
idxTrn = training(cvp); % Training set indices
idxTest = test(cvp);    % Test set indices

Standardize the training data and train the regression kernel model.

Xtrain = X(idxTrn,:);
Ytrain = Y(idxTrn);
[Ztrain,tr_mu,tr_sigma] = zscore(Xtrain); % Standardize the training data
tr_sigma(tr_sigma==0) = 1;
Mdl = fitrkernel(Ztrain,Ytrain)
Mdl = 
              ResponseName: 'Y'
                   Learner: 'svm'
    NumExpansionDimensions: 128
               KernelScale: 1
                    Lambda: 0.0028
             BoxConstraint: 1
                   Epsilon: 0.8617

  Properties, Methods

Mdl is a RegressionKernel model.

Standardize the test data using the same mean and standard deviation of the training data columns. Predict responses for the test set.

Xtest = X(idxTest,:);
Ztest = (Xtest-tr_mu)./tr_sigma; % Standardize the test data
Ytest = Y(idxTest);

YFit = predict(Mdl,Ztest);

Create a table containing the first 10 observed response values and predicted response values.

ans=10×2 table
    ObservedValue    PredictedValue
    _____________    ______________

         18              17.616    
         14              25.799    
         24              24.141    
         25              25.018    
         14              13.637    
         14              14.557    
         18              18.584    
         27              26.096    
         21              25.031    
         13              13.324    

Estimate the test set regression loss using the mean squared error loss function.

L = loss(Mdl,Ztest,Ytest)
L = 9.2664

Input Arguments

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Kernel regression model, specified as a RegressionKernel model object. You can create a RegressionKernel model object using fitrkernel.

Predictor data used to generate responses, specified as a numeric matrix or table.

Each row of X corresponds to one observation, and each column corresponds to one variable.

  • For a numeric matrix:

    • The variables in the columns of X must have the same order as the predictor variables that trained Mdl.

    • If you trained Mdl using a table (for example, Tbl) and Tbl contains all numeric predictor variables, then X can be a numeric matrix. To treat numeric predictors in Tbl as categorical during training, identify categorical predictors using the CategoricalPredictors name-value pair argument of fitrkernel. If Tbl contains heterogeneous predictor variables (for example, numeric and categorical data types) and X is a numeric matrix, then predict throws an error.

  • For a table:

    • predict does not support multicolumn variables or cell arrays other than cell arrays of character vectors.

    • If you trained Mdl using a table (for example, Tbl), then all predictor variables in X must have the same variable names and data types as those that trained Mdl (stored in Mdl.PredictorNames). However, the column order of X does not need to correspond to the column order of Tbl. Also, Tbl and X can contain additional variables (response variables, observation weights, and so on), but predict ignores them.

    • If you trained Mdl using a numeric matrix, then the predictor names in Mdl.PredictorNames and corresponding predictor variable names in X must be the same. To specify predictor names during training, see the PredictorNames name-value pair argument of fitrkernel. All predictor variables in X must be numeric vectors. X can contain additional variables (response variables, observation weights, and so on), but predict ignores them.

Data Types: double | single | table

Output Arguments

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Predicted responses, returned as a numeric vector.

YFit is an n-by-1 vector of the same data type as the response data (Y) used to train Mdl, where n is the number of observations in X.

Extended Capabilities

Introduced in R2018a