# predict

## Description

specifies additional options using one or more name-value arguments. For example, specify
that columns in the predictor data correspond to observations.`yfit`

= predict(`Mdl`

,`X`

,`Name=Value`

)

## 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"`

`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.

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