predict

Predict response of Gaussian process regression model

Syntax

ypred = predict(gprMdl,Xnew)
[ypred,ysd,yint] = predict(gprMdl,Xnew)
[ypred,ysd,yint] = predict(gprMdl,Xnew,'Alpha',alpha)


Description

ypred = predict(gprMdl,Xnew) returns the predicted responses ypred for the Gaussian process regression (GPR) model gprMdl and the predictor values in Xnew.

[ypred,ysd,yint] = predict(gprMdl,Xnew) also returns the standard deviations ysd and 95% prediction intervals yint of the response variable, evaluated at each observation in Xnew using the trained GPR model.

[ypred,ysd,yint] = predict(gprMdl,Xnew,'Alpha',alpha) specifies the significance level for the confidence level of the prediction intervals yint. The confidence level of yint is equal to 100(1 – Alpha)%.

Input Arguments

gprMdl — Gaussian process regression model

RegressionGP object | CompactRegressionGP object

Gaussian process regression model, specified as a RegressionGP (full) or CompactRegressionGP (compact) object.

Xnew — New values for the predictors

table | m-by-d matrix

New values for the predictors that fitrgp uses in training the GPR model, specified as a table or an m-by-d matrix. m is the number of observations and d is the number of predictor variables in the training data.

If you trained gprMdl on a table, then Xnew must be a table that contains all the predictor variables used to train gprMdl.

If you trained gprMdl on a matrix, then Xnew must be a numeric matrix with d columns.

Data Types: single | double | table

alpha — Significance level

0.05 (default) | numeric scalar in [0,1]

Significance level for the confidence level of the prediction intervals yint, specified as a numeric scalar in the range [0,1]. The confidence level of yint is equal to 100(1 – Alpha)%.

Example: 'Alpha',0.01 specifies to return 99% prediction intervals.

Data Types: single | double

Output Arguments

ypred — Predicted responses

column vector

Predicted responses, returned as a column vector of length n, where n is the number of observations in the predictor data Xnew.

ysd — Standard deviations of response variable

column vector

Standard deviations of the response variable, evaluated at each observation in the predictor data Xnew, returned as a column vector of length n, where n is the number of observations in Xnew. The ith element ysd(i) contains the standard deviation of the ith response for the ith observation Xnew(i,:), estimated using the trained GPR model gprMdl.

yint — Prediction intervals of response variable

n-by-2 matrix

Prediction intervals of the response variable, evaluated at each observation in the predictor data Xnew, returned as an n-by-2 matrix, where n is the number of observations in Xnew. The ith row yint(i,:) contains the 100(1 – Alpha)% prediction interval of the ith response for the ith observation Xnew(i,:). The Alpha value is the probability that the prediction interval does not contain the true response value for Xnew(i,:). The first column of yint contains the lower limits of the prediction intervals, and the second column contains the upper limits.

Examples

Compute Predicted Responses

Generate the sample data.

n = 10000;
rng(1) % For reproducibility
x = linspace(0.5,2.5,n)';
y = sin(10*pi.*x) ./ (2.*x)+(x-1).^4 + 1.5*rand(n,1);

Fit a GPR model using the Matern 3/2 kernel function with separate length scale for each predictor and an active set size of 100. Use the subset of regressors approximation method for parameter estimation and fully independent conditional method for prediction.

gprMdl = fitrgp(x,y,'KernelFunction','ardmatern32', ...
    'ActiveSetSize',100,'FitMethod','sr','PredictMethod','fic');

Compute the predictions.

[ypred,~,yci] = predict(gprMdl,x);

Plot the data along with the predictions and prediction intervals.

plot(x,y,'r.')
hold on
plot(x,ypred,'b-')
plot(x,yci(:,1),'k--')
plot(x,yci(:,2),'k--')
xlabel('x')
ylabel('y')
legend('True responses','GPR predictions', ...
    'Prediction interval limits','Location','best')

Compute Predictions When Data in Table

Load the sample data and store in a table.

load fisheriris
tbl = table(meas(:,1),meas(:,2),meas(:,3),meas(:,4),species,...
'VariableNames',{'meas1','meas2','meas3','meas4','species'});

Fit a GPR model using the first measurement as the response and the other variables as the predictors.

mdl = fitrgp(tbl,'meas1');

Compute the predictions and the 99% confidence intervals.

[ypred,~,yci] = predict(mdl,tbl,'Alpha',0.01);

Plot the true response and the predictions along with the prediction intervals.

figure();
plot(mdl.Y,'r.');
hold on;
plot(ypred);
plot(yci(:,1),'k:');
plot(yci(:,2),'k:');
legend('True response','GPR predictions',...
'Lower prediction limit','Upper prediction limit',...
'Location','Best');

Plot Predicted Response for Test Data

Load the sample data.

load('gprdata.mat');

The data contains training and test data. There are 500 observations in training data and 100 observations in test data. The data has 8 predictor variables. This is simulated data.

Fit a GPR model using the squared exponential kernel function with a separate length scale for each predictor. Standardize predictors in the training data. Use the exact fitting and prediction methods.

gprMdl = fitrgp(Xtrain,ytrain,'Basis','constant',...
'FitMethod','exact','PredictMethod','exact',...
'KernelFunction','ardsquaredexponential','Standardize',1);

Predict the responses for test data.

[ytestpred,~,ytestci] = predict(gprMdl,Xtest);

Plot the test response along with the predictions.

figure;
plot(ytest,'r');
hold on;
plot(ytestpred,'b');
plot(ytestci(:,1),'k:');
plot(ytestci(:,2),'k:');
legend('Actual response','GPR predictions',...
'95% lower','95% upper','Location','Best');
hold off

Tips

• You can choose the prediction method while training the GPR model using the PredictMethod name-value pair argument in fitrgp. The default prediction method is 'exact' for n ≤ 10000, where n is the number of observations in the training data, and 'bcd' (block coordinate descent), otherwise.

• Computation of standard deviations, ysd, and prediction intervals, yint, is not supported when PredictMethod is 'bcd'.

• If gprMdl is a CompactRegressionGP object, you cannot compute standard deviations, ysd, or prediction intervals, yint, for PredictMethod equal to 'sr' or 'fic'. To compute ysd and yint for PredictMethod equal to 'sr' or 'fic', use the full regression (RegressionGP) object.

Alternatives

You can use resubPredict to compute the predicted responses for the trained GPR model at the observations in the training data.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Use saveLearnerForCoder, loadLearnerForCoder, and codegen (MATLAB Coder) to generate code for the predict function. Save a trained model by using saveLearnerForCoder. Define an entry-point function that loads the saved model by using loadLearnerForCoder and calls the predict function. Then use codegen to generate code for the entry-point function.

• For single-precision code generation, use standardized data by specifying 'Standardize',true when you train the model. To generate single-precision C/C++ code for predict, specify the name-value argument 'DataType','single' when you call the loadLearnerForCoder function.

• This table contains notes about the arguments of predict. Arguments not included in this table are fully supported.

  Argument	Notes and Limitations
  Mdl	For the usage notes and limitations of the model object, see Code Generation of the CompactRegressionGP object.
  Xnew	Xnew must be a single-precision or double-precision matrix or a table containing numeric variables, categorical variables, or both. The number of rows, or observations, in Xnew can be a variable size, but the number of columns in Xnew must be fixed. If you want to specify Xnew as a table, then your model must be trained using a table, and you must ensure that your entry-point function for prediction: Accepts data as arrays Creates a table from the data input arguments and specifies the variable names in the table Passes the table to predict For an example of this table workflow, see Generate Code to Classify Data in Table. For more information on using tables in code generation, see Code Generation for Tables (MATLAB Coder) and Table Limitations for Code Generation (MATLAB Coder).
  Name-value pair arguments	Names in name-value pair arguments must be compile-time constants. For example, to allow a user-defined significance level in the generated code, include {coder.Constant('Alpha'),0} in the -args value of codegen (MATLAB Coder).

For more information, see Introduction to Code Generation.