predict

Train a generalized additive model using training samples, and then predict the test sample responses.

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);

Randomly partition observations into a training set and a test set. Specify a 10% holdout sample for testing.

rng('default') % For reproducibility
cv = cvpartition(size(tbl,1),'HoldOut',0.10);

Extract the training and test indices.

trainInds = training(cv);
testInds = test(cv);

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

Mdl = fitrgam(tbl(trainInds,:),'Systolic')

Mdl = 
  RegressionGAM
            PredictorNames: {'Age'  'Diastolic'  'Smoker'  'Weight'  'Gender'  'SelfAssessedHealthStatus'}
              ResponseName: 'Systolic'
     CategoricalPredictors: [3 5 6]
         ResponseTransform: 'none'
                 Intercept: 122.7444
    IsStandardDeviationFit: 0
           NumObservations: 90

Mdl is a RegressionGAM model object.

Predict responses for the test set.

yFit = predict(Mdl,tbl(testInds,:));

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

table(tbl.Systolic(testInds),yFit, ...
    'VariableNames',{'Observed Value','Predicted Value'})

ans=10×2 table
    Observed Value    Predicted Value
    ______________    _______________

         124              126.58     
         121              123.95     
         130              116.72     
         115              117.35     
         121              117.45     
         116               118.5     
         123              126.16     
         132              124.14     
         125              127.36     
         124              115.99     

Predict responses for new observations using a generalized additive model that contains both linear and interaction terms for predictors. Use a memory-efficient model object, and 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;

Partition the data set into two sets: one containing training data, and the other containing new, unobserved test data. Reserve 10 observations for the new test data set.

rng('default')
n = size(X,1);
newInds = randsample(n,10);
inds = ~ismember(1:n,newInds);
XNew = X(newInds,:);
YNew = Y(newInds);

Train a GAM that contains all the available linear and interaction terms in X.

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

Mdl is a RegressionGAM model object.

Conserve memory by reducing the size of the trained model.

CMdl = compact(Mdl);
whos('Mdl','CMdl')

  Name      Size              Bytes  Class                                          Attributes

  CMdl      1x1             1255766  classreg.learning.regr.CompactRegressionGAM              
  Mdl       1x1             1289882  RegressionGAM                                            

CMdl is a CompactRegressionGAM 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 = predict(CMdl,XNew);
yFit_nointeraction = predict(CMdl,XNew,'IncludeInteractions',false);

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

t = table(YNew,yFit,yFit_nointeraction, ...
    'VariableNames',{'Observed Response', ...
    'Predicted Response','Predicted Response Without Interactions'})

t=10×3 table
    Observed Response    Predicted Response    Predicted Response Without Interactions
    _________________    __________________    _______________________________________

          27.9                  23.04                          23.649                 
           NaN                 37.163                          35.779                 
           NaN                 25.876                          21.978                 
            13                 12.786                          14.141                 
            36                 28.889                          27.281                 
          19.9                 22.199                          18.451                 
          24.2                 23.995                          24.885                 
            12                 14.247                          13.982                 
            38                 33.797                          33.528                 
            13                 12.225                          11.127                 

Train a generalized additive model (GAM), and then compute and plot the prediction intervals of response values.

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. Specify the FitStandardDeviation name-value argument as true so that you can use the trained model to compute prediction intervals. A recommended practice is to use optimal hyperparameters when you fit the standard deviation model for the accuracy of the standard deviation estimates. Specify 'OptimizeHyperparameters' as 'all-univariate'. For reproducibility, use the 'expected-improvement-plus' acquisition function. Specify 'ShowPlots' as false and 'Verbose' as 0 to disable plot and message displays, respectively.

rng('default') % For reproducibility
Mdl = fitrgam(tbl,'Systolic','FitStandardDeviation',true, ...
    'OptimizeHyperparameters','all-univariate', ...
    'HyperparameterOptimizationOptions',struct('AcquisitionFunctionName','expected-improvement-plus', ...
    'ShowPlots',false,'Verbose',0))

Mdl = 
  RegressionGAM
                       PredictorNames: {'Age'  'Diastolic'  'Smoker'  'Weight'  'Gender'  'SelfAssessedHealthStatus'}
                         ResponseName: 'Systolic'
                CategoricalPredictors: [3 5 6]
                    ResponseTransform: 'none'
                            Intercept: 122.7800
               IsStandardDeviationFit: 1
                      NumObservations: 100
    HyperparameterOptimizationResults: [1x1 BayesianOptimization]

Mdl is a RegressionGAM model object that uses the best estimated feasible point. The best estimated feasible point indicates the set of hyperparameters that minimizes the upper confidence bound of the objective function value based on the underlying objective function model of the Bayesian optimization process. For more details on the optimization process, see Optimize GAM Using OptimizeHyperparameters.

Predict responses for the training data in tbl, and compute the 99% prediction intervals of the response variable. Specify the significance level ('Alpha') as 0.01 to set the confidence level of the prediction intervals to 99%.

[yFit,~,yInt] = predict(Mdl,tbl,'Alpha',0.01);

Plot the sorted true responses together with the predicted responses and prediction intervals.

figure
yTrue = tbl.Systolic;
[sortedYTrue,I] = sort(yTrue); 
plot(sortedYTrue,'o')
hold on
plot(yFit(I))
plot(yInt(I,1),'k:')
plot(yInt(I,2),'k:')
legend('True responses','Predicted responses', ...
    'Prediction interval limits','Location','best')
hold off