predict

Predict responses using regression neural network

Since R2021a

Syntax

yfit = predict(Mdl,X)

yfit = predict(Mdl,X,Name=Value)

Description

yfit = predict(Mdl,X) returns predicted response values for the predictor data in the table or matrix X using the trained regression neural network model Mdl.

yfit = predict(Mdl,X,Name=Value) specifies additional options using one or more name-value arguments. For example, specify that columns in the predictor data correspond to observations.

Examples

Predict Test Set Response Using Regression Neural Network

Predict test set response values by using a trained regression neural network model.

Load the patients data set. Create a table from the data set. Each row corresponds to one patient, and each column corresponds to a diagnostic variable. Use the Systolic variable as the response variable, and the rest of the variables as predictors.

load patients
tbl = table(Diastolic,Height,Smoker,Weight,Systolic);

Separate the data into a training set tblTrain and a test set tblTest by using a nonstratified holdout partition. The software reserves approximately 30% of the observations for the test data set and uses the rest of the observations for the training data set.

rng("default") % For reproducibility of the partition
c = cvpartition(size(tbl,1),"Holdout",0.30);
trainingIndices = training(c);
testIndices = test(c);
tblTrain = tbl(trainingIndices,:);
tblTest = tbl(testIndices,:);

Train a regression neural network model using the training set. Specify the Systolic column of tblTrain as the response variable. Specify to standardize the numeric predictors, and set the iteration limit to 50. By default, the neural network model has one fully connected layer with 10 outputs, excluding the final fully connected layer.

Mdl = fitrnet(tblTrain,"Systolic", ...
    "Standardize",true,"IterationLimit",50);

Predict the systolic blood pressure levels for patients in the test set.

predictedY = predict(Mdl,tblTest);

Visualize the results by using a scatter plot with a reference line. Plot the predicted values along the vertical axis and the true response values along the horizontal axis. Points on the reference line indicate correct predictions.

plot(tblTest.Systolic,predictedY,".")
hold on
plot(tblTest.Systolic,tblTest.Systolic)
hold off
xlabel("True Systolic Blood Pressure Levels")
ylabel("Predicted Systolic Blood Pressure Levels")

Because many of the points are far from the reference line, the default neural network model with a fully connected layer of size 10 does not seem to be a great predictor of systolic blood pressure levels.

Select Features to Include in Regression Neural Network

Perform feature selection by comparing test set losses and predictions. Compare the test set metrics for a regression neural network model trained using all the predictors to the test set metrics for a model trained using only a subset of the predictors.

Load the sample file fisheriris.csv, which contains iris data including sepal length, sepal width, petal length, petal width, and species type. Read the file into a table.

fishertable = readtable('fisheriris.csv');

Separate the data into a training set trainTbl and a test set testTbl by using a nonstratified holdout partition. The software reserves approximately 30% of the observations for the test data set and uses the rest of the observations for the training data set.

rng("default")
c = cvpartition(size(fishertable,1),"Holdout",0.3);
trainTbl = fishertable(training(c),:);
testTbl = fishertable(test(c),:);

Train one regression neural network model using all the predictors in the training set, and train another model using all the predictors except PetalWidth. For both models, specify PetalLength as the response variable, and standardize the predictors.

allMdl = fitrnet(trainTbl,"PetalLength","Standardize",true);
subsetMdl = fitrnet(trainTbl,"PetalLength ~ SepalLength + SepalWidth + Species", ...
    "Standardize",true);

Compare the test set mean squared error (MSE) of the two models. Smaller MSE values indicate better performance.

allMSE = loss(allMdl,testTbl)

allMSE = 
0.0834

subsetMSE = loss(subsetMdl,testTbl)

subsetMSE = 
0.0884

For each model, compare the test set predicted petal lengths to the true petal lengths. Plot the predicted petal lengths along the vertical axis and the true petal lengths along the horizontal axis. Points on the reference line indicate correct predictions.

tiledlayout(2,1)

% Top axes
ax1 = nexttile;
allPredictedY = predict(allMdl,testTbl);
plot(ax1,testTbl.PetalLength,allPredictedY,".")
hold on
plot(ax1,testTbl.PetalLength,testTbl.PetalLength)
hold off
xlabel(ax1,"True Petal Length")
ylabel(ax1,"Predicted Petal Length")
title(ax1,"All Predictors")

% Bottom axes
ax2 = nexttile;
subsetPredictedY = predict(subsetMdl,testTbl);
plot(ax2,testTbl.PetalLength,subsetPredictedY,".")
hold on
plot(ax2,testTbl.PetalLength,testTbl.PetalLength)
hold off
xlabel(ax2,"True Petal Length")
ylabel(ax2,"Predicted Petal Length")
title(ax2,"Subset of Predictors")

Because both models seems to perform well, with predictions scattered near the reference line, consider using the model trained using all predictors except PetalWidth.

Predict Using Layer Structure of Regression Neural Network Model

See how the layers of a regression neural network model work together to predict the response value for a single observation.

Load the sample file fisheriris.csv, which contains iris data including sepal length, sepal width, petal length, petal width, and species type. Read the file into a table, and display the first few rows of the table.

fishertable = readtable('fisheriris.csv');
head(fishertable)

    SepalLength    SepalWidth    PetalLength    PetalWidth     Species  
    ___________    __________    ___________    __________    __________

        5.1           3.5            1.4           0.2        {'setosa'}
        4.9             3            1.4           0.2        {'setosa'}
        4.7           3.2            1.3           0.2        {'setosa'}
        4.6           3.1            1.5           0.2        {'setosa'}
          5           3.6            1.4           0.2        {'setosa'}
        5.4           3.9            1.7           0.4        {'setosa'}
        4.6           3.4            1.4           0.3        {'setosa'}
          5           3.4            1.5           0.2        {'setosa'}

Train a regression neural network model using the data set. Specify the PetalLength variable as the response and use the other numeric variables as predictors.

Mdl = fitrnet(fishertable,"PetalLength ~ SepalLength + SepalWidth + PetalWidth");

Select the fifteenth observation from the data set. See how the layers of the neural network take the observation and return a predicted response value newPointResponse.

newPoint = Mdl.X{15,:}

newPoint = 1×3

    5.8000    4.0000    0.2000

firstFCStep = (Mdl.LayerWeights{1})*newPoint' + Mdl.LayerBiases{1};
reluStep = max(firstFCStep,0);

finalFCStep = (Mdl.LayerWeights{end})*reluStep + Mdl.LayerBiases{end};

newPointResponse = finalFCStep

newPointResponse = 
1.6716

Check that the prediction matches the one returned by the predict object function.

predictedY = predict(Mdl,newPoint)

predictedY = 
1.6716

isequal(newPointResponse,predictedY)

ans = logical
   1

The two results match.

Specify Multiple Response Variables in Neural Network

Since R2024b

Create a regression neural network with more than one response variable.

Load the carbig data set, which contains measurements of cars made in the 1970s and early 1980s. Create a table containing the predictor variables Displacement, Horsepower, and so on, as well as the response variables Acceleration and MPG. Display the first eight rows of the table.

load carbig
cars = table(Displacement,Horsepower,Model_Year, ...
    Origin,Weight,Acceleration,MPG);
head(cars)

    Displacement    Horsepower    Model_Year    Origin     Weight    Acceleration    MPG
    ____________    __________    __________    _______    ______    ____________    ___

        307            130            70        USA         3504           12        18 
        350            165            70        USA         3693         11.5        15 
        318            150            70        USA         3436           11        18 
        304            150            70        USA         3433           12        16 
        302            140            70        USA         3449         10.5        17 
        429            198            70        USA         4341           10        15 
        454            220            70        USA         4354            9        14 
        440            215            70        USA         4312          8.5        14 

Remove rows of cars where the table has missing values.

cars = rmmissing(cars);

Categorize the cars based on whether they were made in the USA.

cars.Origin = categorical(cellstr(cars.Origin));
cars.Origin = mergecats(cars.Origin,["France","Japan",...
    "Germany","Sweden","Italy","England"],"NotUSA");

Partition the data into training and test sets. Use approximately 85% of the observations to train a neural network model, and 15% of the observations to test the performance of the trained model on new data. Use cvpartition to partition the data.

rng("default") % For reproducibility
c = cvpartition(height(cars),"Holdout",0.15);
carsTrain = cars(training(c),:);
carsTest = cars(test(c),:);

Train a multiresponse neural network regression model by passing the carsTrain training data to the fitrnet function. For better results, specify to standardize the predictor data.

Mdl = fitrnet(carsTrain,["Acceleration","MPG"], ...
    Standardize=true)

Mdl = 
  RegressionNeuralNetwork
           PredictorNames: {'Displacement'  'Horsepower'  'Model_Year'  'Origin'  'Weight'}
             ResponseName: {'Acceleration'  'MPG'}
    CategoricalPredictors: 4
        ResponseTransform: 'none'
          NumObservations: 334
               LayerSizes: 10
              Activations: 'relu'
    OutputLayerActivation: 'none'
                   Solver: 'LBFGS'
          ConvergenceInfo: [1x1 struct]
          TrainingHistory: [1000x7 table]

Mdl is a trained RegressionNeuralNetwork model. You can use dot notation to access the properties of Mdl. For example, you can specify Mdl.ConvergenceInfo to get more information about the model convergence.

Evaluate the performance of the regression model on the test set by computing the test mean squared error (MSE). Smaller MSE values indicate better performance. Return the loss for each response variable separately by setting the OutputType name-value argument to "per-response".

testMSE = loss(Mdl,carsTest,["Acceleration","MPG"], ...
    OutputType="per-response")

testMSE = 1×2

    1.5341    4.8245

Predict the response values for the observations in the test set. Return the predicted response values as a table.

predictedY = predict(Mdl,carsTest,OutputType="table")

predictedY=58×2 table
    Acceleration     MPG  
    ____________    ______

       9.3612       13.567
       15.655       21.406
       17.921       17.851
       11.139       13.433
       12.696        10.32
       16.498       17.977
       16.227       22.016
       12.165       12.926
       12.691       12.072
       12.424       14.481
       16.974       22.152
       15.504       24.955
       11.068       13.874
       11.978       12.664
       14.926       10.134
       15.638       24.839
      ⋮

Input Arguments

Mdl — Trained regression neural network

RegressionNeuralNetwork model object | CompactRegressionNeuralNetwork model object

Trained regression neural network, specified as a RegressionNeuralNetwork model object or CompactRegressionNeuralNetwork model object returned by fitrnet or compact, respectively.

X — Predictor data used to generate responses

numeric matrix | table

Predictor data used to generate responses, specified as a numeric matrix or table.

By default, each row of X corresponds to one observation, and each column corresponds to one variable.

• For a numeric matrix:

  • The variables in the columns of X must have the same order as the predictor variables that trained Mdl.

  • If you train Mdl using a table (for example, Tbl) and Tbl contains only numeric predictor variables, then X can be a numeric matrix. To treat numeric predictors in Tbl as categorical during training, identify categorical predictors by using the CategoricalPredictors name-value argument of fitrnet. If Tbl contains heterogeneous predictor variables (for example, numeric and categorical data types) and X is a numeric matrix, then predict throws an error.

• For a table:

  • predict does not support multicolumn variables or cell arrays other than cell arrays of character vectors.

  • If you train Mdl using a table (for example, Tbl), then all predictor variables in X must have the same variable names and data types as the variables that trained Mdl (stored in Mdl.PredictorNames). However, the column order of X does not need to correspond to the column order of Tbl. Also, Tbl and X can contain additional variables (response variables, observation weights, and so on), but predict ignores them.

  • If you train Mdl using a numeric matrix, then the predictor names in Mdl.PredictorNames must be the same as the corresponding predictor variable names in X. To specify predictor names during training, use the PredictorNames name-value argument of fitrnet. All predictor variables in X must be numeric vectors. X can contain additional variables (response variables, observation weights, and so on), but predict ignores them.

If you set Standardize=true in fitrnet when training Mdl, then the software standardizes the numeric columns of the predictor data using the corresponding means (Mdl.Mu) and standard deviations (Mdl.Sigma).

Note

If you orient your predictor matrix so that observations correspond to columns and specify ObservationsIn="columns", then you might experience a significant reduction in computation time. You cannot specify ObservationsIn="columns" for predictor data in a table or for multiresponse regression.

Data Types: single | double | table

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: predict(Mdl,X,ObservationsIn="columns") indicates that columns in the predictor data correspond to observations.

ObservationsIn — Predictor data observation dimension

"rows" (default) | "columns"

Predictor data observation dimension, specified as "rows" or "columns".

Note

If you orient your predictor matrix so that observations correspond to columns and specify ObservationsIn="columns", then you might experience a significant reduction in computation time. You cannot specify ObservationsIn="columns" for predictor data in a table or for multiresponse regression.

Data Types: char | string

OutputType — Output type for predicted responses

"matrix" (default) | "table"

Since R2024b

Output type for the predicted responses yfit, specified as "matrix" or "table". This argument is valid only when Mdl is a model with multiple response variables.

Example: OutputType="table"

Data Types: char | string

PredictionForMissingValue — Predicted response value to use for observations with missing predictor values

"median" (default) | "mean" | numeric scalar

Since R2023b

Predicted response value to use for observations with missing predictor values, specified as "median", "mean", or a numeric scalar.

Value	Description
"median"	predict uses the median of the observed response values in the training data as the predicted response value for observations with missing predictor values.
"mean"	predict uses the mean of the observed response values in the training data as the predicted response value for observations with missing predictor values.
Numeric scalar	predict uses this value as the predicted response value for observations with missing predictor values.

Example: PredictionForMissingValue="mean"

Example: PredictionForMissingValue=NaN

Data Types: single | double | char | string

Output Arguments

yfit — Predicted responses

numeric vector | numeric matrix | numeric table

Predicted responses, returned as a numeric vector, matrix, or table.

• If yfit is a numeric vector, then entry i in yfit corresponds to observation i in X.

• If yfit is a numeric matrix or table, then row i in yfit corresponds to observation i in X.

Alternative Functionality

Simulink Block

To integrate the prediction of a neural network regression model into Simulink^®, you can use the RegressionNeuralNetwork Predict block in the Statistics and Machine Learning Toolbox™ library or a MATLAB^® Function block with the predict function. For examples, see Predict Responses Using RegressionNeuralNetwork Predict Block and Predict Class Labels Using MATLAB Function Block.

When deciding which approach to use, consider the following:

• If you use the Statistics and Machine Learning Toolbox library block, you can use the Fixed-Point Tool (Fixed-Point Designer) to convert a floating-point model to fixed point.

• Support for variable-size arrays must be enabled for a MATLAB Function block with the predict function.

• If you use a MATLAB Function block, you can use MATLAB functions for preprocessing or post-processing before or after predictions in the same MATLAB Function block.

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. Code generation is not supported for multiresponse regression.

• 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 CompactRegressionNeuralNetwork object.
  X	X 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 X can be a variable size, but the number of columns in X must be fixed. If you want to specify X as a table, then your model must be trained using a table, and your entry-point function for prediction must do the following: Accept data as arrays. Create a table from the data input arguments and specify the variable names in the table. Pass 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 arguments	Names in name-value arguments must be compile-time constants. The ObservationsIn value must be a compile-time constant. For example, to use ObservationsIn="columns" in the generated code, include {coder.Constant("ObservationsIn"),coder.Constant("columns")} in the -args value of codegen (MATLAB Coder). The OutputType name-value argument is not supported for code generation. If the value of PredictionForMissingValue is nonnumeric, then it must be a compile-time constant.

For more information, see Introduction to Code Generation.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™. (since R2024b)

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

Version History

Introduced in R2021a

R2024b: Make predictions for neural network regression model trained with multiple response variables

You can create a neural network regression model with multiple response variables by using the fitrnet function. Regardless of the number of response variables, the function returns a RegressionNeuralNetwork object. You can use the predict object function to predict the responses for new data.

In the call to predict, you can specify whether to return the predicted response values as a matrix or table by using the OutputType name-value argument.

R2024b: Specify GPU arrays (requires Parallel Computing Toolbox)

predict fully supports GPU arrays.

R2023b: Specify predicted response value to use for observations with missing predictor values

Starting in R2023b, when you predict or compute the loss, some regression models allow you to specify the predicted response value for observations with missing predictor values. Specify the PredictionForMissingValue name-value argument to use a numeric scalar, the training set median, or the training set mean as the predicted value. When computing the loss, you can also specify to omit observations with missing predictor values.

This table lists the object functions that support the PredictionForMissingValue name-value argument. By default, the functions use the training set median as the predicted response value for observations with missing predictor values.

Model Type	Model Objects	Object Functions
Gaussian process regression (GPR) model	RegressionGP, CompactRegressionGP	loss, predict, resubLoss, resubPredict
	RegressionPartitionedGP	kfoldLoss, kfoldPredict
Gaussian kernel regression model	RegressionKernel	loss, predict
	RegressionPartitionedKernel	kfoldLoss, kfoldPredict
Linear regression model	RegressionLinear	loss, predict
	RegressionPartitionedLinear	kfoldLoss, kfoldPredict
Neural network regression model	RegressionNeuralNetwork, CompactRegressionNeuralNetwork	loss, predict, resubLoss, resubPredict
	RegressionPartitionedNeuralNetwork	kfoldLoss, kfoldPredict
Support vector machine (SVM) regression model	RegressionSVM, CompactRegressionSVM	loss, predict, resubLoss, resubPredict
	RegressionPartitionedSVM	kfoldLoss, kfoldPredict

In previous releases, the regression model loss and predict functions listed above used NaN predicted response values for observations with missing predictor values. The software omitted observations with missing predictor values from the resubstitution ("resub") and cross-validation ("kfold") computations for prediction and loss.