loss
Description
returns the regression loss for the trained regression neural network
L
= loss(Mdl
,Tbl
,ResponseVarName
)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.
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.L
= loss(___,Name,Value
)
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 trainMdl
, then you do not need to specifyResponseVarName
orY
.If you trained
Mdl
using sample data contained in a table, then the input data forloss
must also be in a table.If you set
'Standardize',true
infitrnet
when trainingMdl
, 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
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 inTbl
orX
.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 R2021aR2022a: 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 |
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