Loss for regression neural network
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
L = loss(___,
Test Set Mean Squared Error of Neural Network
Calculate the test set mean squared error (MSE) of a regression neural network model.
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
Mdl — Trained regression neural network
RegressionNeuralNetwork model object |
CompactRegressionNeuralNetwork model object
Tbl — Sample data
Sample data, specified as a table. Each row of
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 you trained
Mdlusing sample data contained in a table, then the input data for
lossmust also be in a table.
If you set
Mdl, then the software standardizes the numeric columns of the predictor data using the corresponding means and standard deviations.
ResponseVarName — Response variable name
name of variable in
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
'Y'. Otherwise, the software treats all columns of
Tbl.Y, as predictors.
X — Predictor data
Predictor data, specified as a numeric matrix. By default,
loss assumes that each row of
corresponds to one observation, and each column corresponds to one predictor
If you orient your predictor matrix so that observations correspond to columns and
'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
Mdl, then the software standardizes the numeric
columns of the predictor data using the corresponding means and standard
Specify optional pairs of arguments as
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.
loss(Mdl,Tbl,"Response","Weights","W") specifies to use the
W variables in the table
Tbl as the response values and observation weights,
PredictionForMissingValue — Predicted response value to use for observations with missing predictor values
"median" (default) |
"omitted" | numeric scalar
Predicted response value to use for observations with missing predictor values,
"omitted", or a numeric scalar.
If an observation is missing all predictor values, an observed response value, or an
observation weight, then
loss does not use the observation
in the loss computation.
Weights — Observation weights
nonnegative numeric vector | name of variable in
Observation weights, specified as a nonnegative numeric vector or the name of a
Tbl. The software weights each observation in
Tbl with the corresponding value in
Weights. The length of
Weights must equal
the number of observations in
If you specify the input data as a table
Weights can be the name of a variable in
Tbl that contains a numeric vector. In this case, you must
Weights as a character vector or string scalar. For
example, if the weights vector
W is stored as
Tbl.W, then specify it as
n is the number of observations in
If you supply weights, then
loss computes the weighted
regression loss and normalizes weights to sum to 1.
Version HistoryIntroduced in R2021a
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|
|Gaussian kernel regression model|
|Linear regression model|
|Neural network regression model|
|Support vector machine (SVM) regression model|
In previous releases, the regression model
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.