predict

Predict responses of generalized linear regression model

Syntax

ypred = predict(mdl,Xnew)

[ypred,yci] = predict(mdl,Xnew)

[ypred,yci] = predict(mdl,Xnew,Name,Value)

Description

ypred = predict(mdl,Xnew) returns the predicted response values of the generalized linear regression model mdl to the points in Xnew.

[ypred,yci] = predict(mdl,Xnew) also returns confidence intervals for the responses at Xnew.

[ypred,yci] = predict(mdl,Xnew,Name,Value) specifies additional options using one or more name-value pair arguments. For example, you can specify the confidence level of the confidence interval.

Examples

Predict Response Values

Create a generalized linear regression model, and predict its response to new data.

Generate sample data using Poisson random numbers with two underlying predictors X(:,1) and X(:,2).

rng('default') % For reproducibility
rndvars = randn(100,2);
X = [2 + rndvars(:,1),rndvars(:,2)];
mu = exp(1 + X*[1;2]);
y = poissrnd(mu);

Create a generalized linear regression model of Poisson data.

mdl = fitglm(X,y,'y ~ x1 + x2','Distribution','poisson');

Create data points for prediction.

[Xtest1,Xtest2] = meshgrid(-1:.5:3,-2:.5:2);
Xnew = [Xtest1(:),Xtest2(:)];

Predict responses at the data points.

ypred = predict(mdl,Xnew);

Plot the predictions.

surf(Xtest1,Xtest2,reshape(ypred,9,9))

Generate C/C++ Code for Prediction

Fit a generalized linear regression model, and then save the model by using saveLearnerForCoder. Define an entry-point function that loads the model by using loadLearnerForCoder and calls the predict function of the fitted model. Then use codegen (MATLAB Coder) to generate C/C++ code. Note that generating C/C++ code requires MATLAB® Coder™.

This example briefly explains the code generation workflow for the prediction of linear regression models at the command line. For more details, see Code Generation for Prediction of Machine Learning Model at Command Line. You can also generate code using the MATLAB Coder app. For details, see Code Generation for Prediction of Machine Learning Model Using MATLAB Coder App.

Train Model

Generate sample data using Poisson random numbers with two underlying predictors X(:,1) and X(:,2).

rng('default') % For reproducibility
rndvars = randn(100,2);
X = [2 + rndvars(:,1),rndvars(:,2)];
mu = exp(1 + X*[1;2]);
y = poissrnd(mu);

Create a generalized linear regression model. Specify the Poisson distribution for the response.

mdl = fitglm(X,y,'y ~ x1 + x2','Distribution','poisson');

Save Model

Save the fitted generalized linear regression model to the file GLMMdl.mat by using saveLearnerForCoder.

saveLearnerForCoder(mdl,'GLMMdl');

Define Entry-Point Function

In your current folder, define an entry-point function named mypredictGLM.m that does the following:

• Accept new predictor input and valid name-value pair arguments.

• Load the fitted generalized linear regression model in GLMMdl.mat by using loadLearnerForCoder.

• Return predictions and confidence interval bounds.

function [yhat,ci] = mypredictGLM(x,varargin) %#codegen
%MYPREDICTGLM Predict responses using GLM model 
%   MYPREDICTGLM predicts responses for the n observations in the n-by-1
%   vector x using the GLM model stored in the MAT-file GLMMdl.mat,
%   and then returns the predictions in the n-by-1 vector yhat.
%   MYPREDICTGLM also returns confidence interval bounds for the
%   predictions in the n-by-2 vector ci.
CompactMdl = loadLearnerForCoder('GLMMdl');
narginchk(1,Inf);
[yhat,ci] = predict(CompactMdl,x,varargin{:});
end

Add the %#codegen compiler directive (or pragma) to the entry-point function after the function signature to indicate that you intend to generate code for the MATLAB algorithm. Adding this directive instructs the MATLAB Code Analyzer to help you diagnose and fix violations that would result in errors during code generation.

Generate Code

Generate code for the entry-point function using codegen (MATLAB Coder). Because C and C++ are statically typed languages, you must determine the properties of all variables in the entry-point function at compile time. To specify the data type and exact input array size, pass a MATLAB® expression that represents the set of values with a certain data type and array size. Use coder.Constant (MATLAB Coder) for the names of name-value pair arguments.

Create points for prediction.

[Xtest1,Xtest2] = meshgrid(-1:.5:3,-2:.5:2);
Xnew = [Xtest1(:),Xtest2(:)];

Generate code and specify returning 90% simultaneous confidence intervals on the predictions.

codegen mypredictGLM -args {Xnew,coder.Constant('Alpha'),0.1,coder.Constant('Simultaneous'),true}

Code generation successful.

codegen generates the MEX function mypredictGLM_mex with a platform-dependent extension.

If the number of observations is unknown at compile time, you can also specify the input as variable-size by using coder.typeof (MATLAB Coder). For details, see Specify Variable-Size Arguments for Code Generation and Specify Properties of Entry-Point Function Inputs (MATLAB Coder).

Verify Generated Code

Compare predictions and confidence intervals using predict and mypredictGLM_mex. Specify name-value pair arguments in the same order as in the -args argument in the call to codegen.

[yhat1,ci1] = predict(mdl,Xnew,'Alpha',0.1,'Simultaneous',true);
[yhat2,ci2] = mypredictGLM_mex(Xnew,'Alpha',0.1,'Simultaneous',true);

The returned values from mypredictGLM_mex might include round-off differences compared to the values from predict. In this case, compare the values allowing a small tolerance.

find(abs(yhat1-yhat2) > 1e-6)

ans =

  0x1 empty double column vector

find(abs(ci1-ci2) > 1e-6)

ans =

  0x1 empty double column vector

The comparison confirms that the returned values are equal within the tolerance 1e–6.

Input Arguments

mdl — Generalized linear regression model

GeneralizedLinearModel object | CompactGeneralizedLinearModel object

Generalized linear regression model, specified as a GeneralizedLinearModel object created using fitglm or stepwiseglm, or a CompactGeneralizedLinearModel object created using compact.

Xnew — New predictor input values

table | dataset array | matrix

New predictor input values, specified as a table, dataset array, or matrix. Each row of Xnew corresponds to one observation, and each column corresponds to one variable.

• If Xnew is a table or dataset array, it must contain predictors that have the same predictor names as in the PredictorNames property of mdl.

• If Xnew is a matrix, it must have the same number of variables (columns) in the same order as the predictor input used to create mdl. Note that Xnew must also contain any predictor variables that are not used as predictors in the fitted model. Also, all variables used in creating mdl must be numeric. To treat numerical predictors as categorical, identify the predictors using the 'CategoricalVars' name-value pair argument when you create mdl.

Data Types: single | double | table

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: [ypred,yci] = predict(Mdl,Xnew,'Alpha',0.01,'Simultaneous',true) returns the confidence interval yci with a 99% confidence level, computed simultaneously for all predictor values.

'Alpha' — Significance level

0.05 (default) | numeric value in the range [0,1]

Significance level for the confidence interval, specified as the comma-separated pair consisting of 'Alpha' and a numeric value in the range [0,1]. The confidence level of yci is equal to 100(1 – Alpha)%. Alpha is the probability that the confidence interval does not contain the true value.

Example: 'Alpha',0.01

Data Types: single | double

'BinomialSize' — Number of trials for binomial distribution

1 (default) | scalar | vector

Number of trials for the binomial distribution, specified as the comma-separated pair consisting of 'BinomialSize' and a scalar or vector of the same length as the response. predict expands the scalar input into a constant array of the same size as the response. The scalar input means that all observations have the same number of trials.

The meaning of the output values in ypred depends on the value of 'BinomialSize'.

• If 'BinomialSize' is 1 (default), then each value in the output ypred is the probability of success.

• If 'BinomialSize' is not 1, then each value in the output ypred is the predicted number of successes in the trials.

Data Types: single | double

'Offset' — Offset value

zeros(size(Xnew,1)) (default) | scalar | vector

Offset value for each row in Xnew, specified as the comma-separated pair consisting of 'Offset' and a scalar or vector with the same length as the response. predict expands the scalar input into a constant array of the same size as the response.

Note that the default value of this argument is a vector of zeros even if you specify the 'Offset' name-value pair argument when fitting a model. If you specify 'Offset' for fitting, the software treats the offset as an additional predictor with a coefficient value fixed at 1. In other words, the formula for fitting is

f(μ) = Offset + X*b,

where f is the link function, μ is the mean response, and X*b is the linear combination of predictors X. The Offset predictor has coefficient 1.

Data Types: single | double

'Simultaneous' — Flag to compute simultaneous confidence bounds

false (default) | true

Flag to compute simultaneous confidence bounds, specified as the comma-separated pair consisting of 'Simultaneous' and either true or false.

• true — predict computes confidence bounds for the curve of response values corresponding to all predictor values in Xnew, using Scheffe's method. The range between the upper and lower bounds contains the curve consisting of true response values with 100(1 – α)% confidence.

• false — predict computes confidence bounds for the response value at each observation in Xnew. The confidence interval for a response value at a specific predictor value contains the true response value with 100(1 – α)% confidence.

Simultaneous bounds are wider than separate bounds, because requiring the entire curve of response values to be within the bounds is stricter than requiring the response value at a single predictor value to be within the bounds.

Example: 'Simultaneous',true

Output Arguments

ypred — Predicted response values

numeric vector

Predicted response values at Xnew, returned as a numeric vector.

For a binomial model, the meaning of the output values in ypred depends on the value of the 'BinomialSize' name-value pair argument.

• If 'BinomialSize' is 1 (default), then each value in the output ypred is the probability of success.

• If 'BinomialSize' is not 1, then each value in the output ypred is the predicted number of successes in the trials.

For a model with an offset, specify the offset value by using the 'Offset' name-value pair argument. Otherwise, predict uses 0 as the offset value.

yci — Confidence intervals for responses

two-column numeric matrix

Confidence intervals for the responses, returned as a two-column matrix with each row providing one interval. The meaning of the confidence interval depends on the settings of the name-value pair arguments 'Alpha' and 'Simultaneous'.

Alternative Functionality

• feval returns the same predictions as predict. The feval function does not support the 'Offset' and 'BinomialSize' name-value pair arguments . feval uses 0 as the offset value, and the output values in ypred are predicted probabilities. The feval function can take multiple input arguments for new predictor input values, with one input for each predictor variable, which is simpler to use with a model created from a table or dataset array. Note that the feval function does not give confidence intervals on its predictions.

• random returns predictions with added noise.

Extended Capabilities

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.

• 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 CompactGeneralizedLinearModel 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.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

• This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

• This function supports model objects fitted with GPU array input arguments.