loss

Loss for regression neural network

Since R2021a

Syntax

L = loss(Mdl,Tbl,ResponseVarName)

L = loss(Mdl,Tbl,Y)

L = loss(Mdl,X,Y)

L = loss(___,Name,Value)

Description

L = loss(Mdl,Tbl,ResponseVarName) returns the regression loss for the trained regression neural network Mdl using the predictor data in table Tbl and the response values in the ResponseVarName table variable.

L is returned as a scalar value that represents the mean squared error (MSE) by default.

L = loss(Mdl,Tbl,Y) returns the regression loss for the model Mdl using the predictor data in table Tbl and the response values in vector Y.

L = loss(Mdl,X,Y) returns the regression loss for the trained regression neural network Mdl using the predictor data X and the corresponding response values in Y.

L = loss(___,Name,Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in previous syntaxes. For example, you can specify that columns in the predictor data correspond to observations, specify the loss function, or supply observation weights.

Note

If the predictor data X or the predictor variables in Tbl contain any missing values, the loss function can return NaN. For more details, see loss can return NaN for predictor data with missing values.

Examples

Test Set Mean Squared Error of Neural Network

Calculate the test set mean squared error (MSE) of a 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.

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

Calculate the test set MSE. Smaller MSE values indicate better performance.

testMSE = loss(Mdl,tblTest,"Systolic")

testMSE = 22.2447

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.

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.

Tbl — Sample data

table

Sample data, specified as a table. Each row of Tbl corresponds to one observation, and each column corresponds to one predictor variable. Optionally, Tbl can contain an additional column for the response variable. Tbl must contain all of the predictors used to train Mdl. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

• If Tbl contains the response variable used to train Mdl, then you do not need to specify ResponseVarName or Y.

• If you trained Mdl using sample data contained in a table, then the input data for loss must also be in a table.

• 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.

Data Types: table

ResponseVarName — Response variable name

name of variable in Tbl

Response variable name, specified as the name of a variable in Tbl. The response variable must be a numeric vector.

If you specify ResponseVarName, then you must specify it as a character vector or string scalar. For example, if the response variable is stored as Tbl.Y, then specify ResponseVarName as 'Y'. Otherwise, the software treats all columns of Tbl, including Tbl.Y, as predictors.

Data Types: char | string

Y — Response data

numeric vector

Response data, specified as a numeric vector. The length of Y must be equal to the number of observations in X or Tbl.

Data Types: single | double

X — Predictor data

numeric matrix

Predictor data, specified as a numeric matrix. By default, loss assumes that each row of X corresponds to one observation, and each column corresponds to one predictor variable.

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.

The length of Y and the number of observations in X must be equal.

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.

Data Types: single | double

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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: loss(Mdl,Tbl,"Response","Weights","W") specifies to use the Response and W variables in the table Tbl as the response values and observation weights, respectively.

LossFun — Loss function

'mse' (default) | function handle

Loss function, specified as 'mse' or a function handle.

• 'mse' — Weighted mean squared error.

• Function handle — To specify a custom loss function, use a function handle. The function must have this form:

  lossval = lossfun(Y,YFit,W)

  • The output argument lossval is a floating-point scalar.

  • You specify the function name (lossfun).

  • Y is a length n numeric vector of observed responses, where n is the number of observations in Tbl or X.

  • YFit is a length n numeric vector of corresponding predicted responses.

  • W is an n-by-1 numeric vector of observation weights.

Example: 'LossFun',@lossfun

Data Types: char | string | function_handle

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.

Data Types: char | string

Weights — Observation weights

nonnegative numeric vector | name of variable in Tbl

Observation weights, specified as a nonnegative numeric vector or the name of a variable in Tbl. The software weights each observation in X or Tbl with the corresponding value in Weights. The length of Weights must equal the number of observations in X or Tbl.

If you specify the input data as a table Tbl, then Weights can be the name of a variable in Tbl that contains a numeric vector. In this case, you must specify Weights as a character vector or string scalar. For example, if the weights vector W is stored as Tbl.W, then specify it as 'W'.

By default, Weights is ones(n,1), where n is the number of observations in X or Tbl.

If you supply weights, then loss computes the weighted regression loss and normalizes weights to sum to 1.

Data Types: single | double | char | string

Version History

Introduced in R2021a

R2022a: loss can return NaN for predictor data with missing values

The loss function no longer omits an observation with a NaN prediction when computing the weighted average regression loss. Therefore, loss can now return NaN when the predictor data X or the predictor variables in Tbl contain any missing values. In most cases, if the test set observations do not contain missing predictors, the loss function does not return NaN.

This change improves the automatic selection of a regression model when you use fitrauto. Before this change, the software might select a model (expected to best predict the responses for new data) with few non-NaN predictors.

If loss in your code returns NaN, you can update your code to avoid this result. Remove or replace the missing values by using rmmissing or fillmissing, respectively.

The following table shows the regression models for which the loss object function might return NaN. For more details, see the Compatibility Considerations for each loss function.

Model Type	Full or Compact Model Object	loss Object Function
Gaussian process regression (GPR) model	RegressionGP, CompactRegressionGP	loss
Gaussian kernel regression model	RegressionKernel	loss
Linear regression model	RegressionLinear	loss
Neural network regression model	RegressionNeuralNetwork, CompactRegressionNeuralNetwork	loss
Support vector machine (SVM) regression model	RegressionSVM, CompactRegressionSVM	loss