resubPredict
Predict responses for training data using trained regression model
Syntax
Description
yFit = resubPredict(Mdl,Name=Value)IncludeInteractions=true specifies to include interaction terms in
computations for generalized additive models.
[
also returns the standard deviations and prediction intervals of the response variable,
evaluated at each observation in the predictor data yFit,ySD,yInt] = resubPredict(___)Mdl.X, using any of
the input argument combinations in the previous syntaxes. This syntax applies only to
generalized additive models for which IsStandardDeviationFit is true, and to Gaussian process
regression models for which the PredictMethod is not
'bcd'.
Examples
Train a generalized additive model (GAM), then predict responses for the training data.
Load the patients data set.
load patientsCreate 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
Properties, Methods
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 carbigSpecify 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
Input Arguments
Name-Value Arguments
Output Arguments
Algorithms
resubPredict predicts responses according to the corresponding
predict function of the object (Mdl). For a
model-specific description, see the predict function reference pages in
the following table.
| Model | Regression Model Object (Mdl) | predict Object Function |
|---|---|---|
| Gaussian process regression model | RegressionGP | predict |
| Generalized additive model | RegressionGAM | predict |
| Neural network model | RegressionNeuralNetwork | predict |
Alternative Functionality
To compute the predicted responses for new predictor data, use the corresponding
predict function of the object (Mdl).
