resubPredict

Train a generalized additive model (GAM), then predict responses for the training data.

Load the patients data set.

load patients

Create a table that contains the predictor variables (Age, Diastolic, Smoker, Weight, Gender, SelfAssessedHealthStatus) and the response variable (Systolic).

tbl = table(Age,Diastolic,Smoker,Weight,Gender,SelfAssessedHealthStatus,Systolic);

Train a univariate GAM that contains the linear terms for the predictors in tbl.

Mdl = fitrgam(tbl,"Systolic")

Mdl = 
  RegressionGAM
            PredictorNames: {'Age'  'Diastolic'  'Smoker'  'Weight'  'Gender'  'SelfAssessedHealthStatus'}
              ResponseName: 'Systolic'
     CategoricalPredictors: [3 5 6]
         ResponseTransform: 'none'
                 Intercept: 122.7800
    IsStandardDeviationFit: 0
           NumObservations: 100

Mdl is a RegressionGAM model object.

Predict responses for the training set.

yFit = resubPredict(Mdl);

Create a table containing the observed response values and the predicted response values. Display the first eight rows of the table.

t = table(tbl.Systolic,yFit, ...
    'VariableNames',{'Observed Value','Predicted Value'});
head(t)

    Observed Value    Predicted Value
    ______________    _______________

         124              124.75     
         109              109.48     
         125              122.89     
         117              115.87     
         122              121.61     
         121              122.02     
         130              126.39     
         115              115.95     

Train a Gaussian process regression (GPR) model by using the fitrgp function. Then predict responses for the training data and estimate prediction intervals of the responses at each observation in the training data by using the resubPredict function.

Generate a training data set.

rng(1) % For reproducibility
n = 100000;
X = linspace(0,1,n)';
X = [X,X.^2];
y = 1 + X*[1;2] + sin(20*X*[1;-2]) + 0.2*randn(n,1);

Train a GPR model using the squared exponential kernel function. Estimate parameters by using the subset of regressors ('sr') approximation method, and make predictions using the subset of data ('sd') method. Use 50 points in the active set, and specify 'sgma' (sparse greedy matrix approximation) method for active set selection. Because the scales of the first and second predictors are different, standardize the data set.

gprMdl = fitrgp(X,y,'KernelFunction','squaredExponential', ...
    'FitMethod','sr','PredictMethod','sd', ...
    'ActiveSetSize',50,'ActiveSetMethod','sgma','Standardize',true);

fitrgp accepts any combination of fitting, prediction, and active set selection methods. However, if you train a model using the block coordinate descent prediction method ('PredictMethod','bcd'), you cannot use the model to compute the standard deviations of the predicted responses; therefore, you also cannot use the model to compute the prediction intervals. For more details, see Tips.

Use the trained model to predict responses for the training data and to estimate the prediction intervals of the predicted responses.

[ypred,~,yci] = resubPredict(gprMdl);

Plot the true responses, predicted responses, and prediction intervals.

figure
plot(y,'r')
hold on
plot(ypred,'b')
plot(yci(:,1),'k--')
plot(yci(:,2),'k--')
legend('True responses','GPR predictions','95% prediction limits','Location','Best')
xlabel('X')
ylabel('y')
hold off

Compute the mean squared error loss on the training data using the trained GPR model.

L = resubLoss(gprMdl)

L = 
0.0523

Predict responses for a training data set using a generalized additive model (GAM) that contains both linear and interaction terms for predictors. Specify whether to include interaction terms when predicting responses.

Load the carbig data set, which contains measurements of cars made in the 1970s and early 1980s.

load carbig

Specify Acceleration, Displacement, Horsepower, and Weight as the predictor variables (X) and MPG as the response variable (Y).

X = [Acceleration,Displacement,Horsepower,Weight];
Y = MPG;

Train a generalized additive model that contains all the available linear and interaction terms in X.

Mdl = fitrgam(X,Y,'Interactions','all');

Mdl is a RegressionGAM model object.

Predict the responses using both linear and interaction terms, and then using only linear terms. To exclude interaction terms, specify 'IncludeInteractions',false.

yFit = resubPredict(Mdl);
yFit_nointeraction = resubPredict(Mdl,'IncludeInteractions',false);

Create a table containing the observed response values and the predicted response values. Display the first eight rows of the table.

t = table(Mdl.Y,yFit,yFit_nointeraction, ...
    'VariableNames',{'Observed Response', ...
    'Predicted Response','Predicted Response Without Interactions'});
head(t)

    Observed Response    Predicted Response    Predicted Response Without Interactions
    _________________    __________________    _______________________________________

           18                  18.026                           17.22                 
           15                  15.003                          15.791                 
           18                  17.663                           16.18                 
           16                  16.178                          15.536                 
           17                  17.107                          17.361                 
           15                  14.943                          14.424                 
           14                  14.119                          14.981                 
           14                  13.864                          13.498