# predict

Predict responses using regression neural network

## Description

## 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(Age,Diastolic,Gender,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. 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);

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 = 0.0856

subsetMSE = loss(subsetMdl,testTbl)

subsetMSE = 0.0881

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)
```

`ans=`*8×5 table*
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.

## 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 and standard
deviations.

**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.

**Data Types: **`single`

| `double`

| `table`

`dimension`

— 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.

**Data Types: **`char`

| `string`

## See Also

`fitrnet`

| `RegressionNeuralNetwork`

| `loss`

| `CompactRegressionNeuralNetwork`

**Introduced in R2021a**

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