fitrnet
Syntax
Description
Use fitrnet
to train a feedforward, fully connected neural
network for regression. The first fully connected layer of the neural network has a connection
from the network input (predictor data), and each subsequent layer has a connection from the
previous layer. Each fully connected layer multiplies the input by a weight matrix and then
adds a bias vector. An activation function follows each fully connected layer, excluding the
last. The final fully connected layer produces the network's output, namely predicted response
values. For more information, see Neural Network Structure.
returns a neural network regression model Mdl
= fitrnet(Tbl
,ResponseVarName
)Mdl
trained using the
predictors in the table Tbl
and the response values in the
ResponseVarName
table variable.
You can use an array
ResponseVarName
to specify multiple response variables. (since R2024b)
returns a neural network regression model trained using the sample data in the table
Mdl
= fitrnet(Tbl
,formula
)Tbl
. The input argument formula
is an
explanatory model of the response and a subset of the predictor variables in
Tbl
used to fit Mdl
.
You can use formula
to
specify multiple response variables. (since R2024b)
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 adjust the number of
outputs and the activation functions for the fully connected layers by specifying the
Mdl
= fitrnet(___,Name=Value
)LayerSizes
and Activations
name-value
arguments.
Convergence control, cross-validation, and hyperparameter optimization options are not supported for multiresponse regression.
[
also returns Mdl
,AggregateOptimizationResults
] = fitrnet(___)AggregateOptimizationResults
, which contains
hyperparameter optimization results when you specify the
OptimizeHyperparameters
and
HyperparameterOptimizationOptions
name-value arguments. You must
also specify the ConstraintType
and
ConstraintBounds
options of
HyperparameterOptimizationOptions
. You can use this syntax to
optimize on compact model size instead of cross-validation loss, and to perform a set of
multiple optimization problems that have the same options but different constraint
bounds.
Hyperparameter optimization options are not supported for multiresponse regression.
Examples
Train Neural Network Regression Model
Train a neural network regression model, and assess the performance of the model on a test set.
Load the carbig
data set, which contains measurements of cars made in the 1970s and early 1980s. Create a table containing the predictor variables Acceleration
, Displacement
, and so on, as well as the response variable MPG
.
load carbig cars = table(Acceleration,Displacement,Horsepower, ... Model_Year,Origin,Weight,MPG);
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 80% of the observations to train a neural network model, and 20% of the observations to test the performance of the trained model on new data. Use cvpartition
to partition the data.
rng("default") % For reproducibility of the data partition c = cvpartition(height(cars),"Holdout",0.20); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
Train a 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,"MPG","Standardize",true)
Mdl = RegressionNeuralNetwork PredictorNames: {'Acceleration' 'Displacement' 'Horsepower' 'Model_Year' 'Origin' 'Weight'} ResponseName: 'MPG' CategoricalPredictors: 5 ResponseTransform: 'none' NumObservations: 314 LayerSizes: 10 Activations: 'relu' OutputLayerActivation: 'none' Solver: 'LBFGS' ConvergenceInfo: [1x1 struct] TrainingHistory: [708x7 table]
Mdl
is a trained RegressionNeuralNetwork
model. You can use dot notation to access the properties of Mdl
. For example, you can specify Mdl.TrainingHistory
to get more information about the training history of the neural network model.
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.
testMSE = loss(Mdl,carsTest,"MPG")
testMSE = 7.1092
Specify Neural Network Regression Model Architecture
Specify the structure of the neural network regression model, including the size of the fully connected layers.
Load the carbig
data set, which contains measurements of cars made in the 1970s and early 1980s. Create a matrix X
containing the predictor variables Acceleration
, Cylinders
, and so on. Store the response variable MPG
in the variable Y
.
load carbig
X = [Acceleration Cylinders Displacement Weight];
Y = MPG;
Delete rows of X
and Y
where either array has missing values.
R = rmmissing([X Y]); X = R(:,1:end-1); Y = R(:,end);
Partition the data into training data (XTrain
and YTrain
) and test data (XTest
and YTest
). Reserve approximately 20% of the observations for testing, and use the rest of the observations for training.
rng("default") % For reproducibility of the partition c = cvpartition(length(Y),"Holdout",0.20); trainingIdx = training(c); % Indices for the training set XTrain = X(trainingIdx,:); YTrain = Y(trainingIdx); testIdx = test(c); % Indices for the test set XTest = X(testIdx,:); YTest = Y(testIdx);
Train a neural network regression model. Specify to standardize the predictor data, and to have 30 outputs in the first fully connected layer and 10 outputs in the second fully connected layer. By default, both layers use a rectified linear unit (ReLU) activation function. You can change the activation functions for the fully connected layers by using the Activations
name-value argument.
Mdl = fitrnet(XTrain,YTrain,"Standardize",true, ... "LayerSizes",[30 10])
Mdl = RegressionNeuralNetwork ResponseName: 'Y' CategoricalPredictors: [] ResponseTransform: 'none' NumObservations: 319 LayerSizes: [30 10] Activations: 'relu' OutputLayerActivation: 'none' Solver: 'LBFGS' ConvergenceInfo: [1x1 struct] TrainingHistory: [1000x7 table]
Access the weights and biases for the fully connected layers of the trained model by using the LayerWeights
and LayerBiases
properties of Mdl
. The first two elements of each property correspond to the values for the first two fully connected layers, and the third element corresponds to the values for the final fully connected layer for regression. For example, display the weights and biases for the first fully connected layer.
Mdl.LayerWeights{1}
ans = 30×4
0.0123 0.0117 -0.0094 0.1175
-0.4081 -0.7849 -0.7201 -2.1720
0.6041 0.1680 -2.3952 0.0934
-3.2332 -2.8360 -1.8264 -1.5723
0.5851 1.5370 1.4623 0.6742
-0.2106 1.2830 -1.7489 -1.5556
0.4800 0.1012 -1.0044 -0.7959
1.8015 -0.5272 -0.7670 0.7496
-1.1428 -0.9902 0.2436 1.2288
-0.0833 -2.4265 0.8388 1.8597
⋮
Mdl.LayerBiases{1}
ans = 30×1
-0.4450
-0.8751
-0.3872
-1.1345
0.4499
-2.1555
2.2111
1.2040
-1.4595
0.4639
⋮
The final fully connected layer has one output. The number of layer outputs corresponds to the first dimension of the layer weights and layer biases.
size(Mdl.LayerWeights{end})
ans = 1×2
1 10
size(Mdl.LayerBiases{end})
ans = 1×2
1 1
To estimate the performance of the trained model, compute the test set mean squared error (MSE) for Mdl
. Smaller MSE values indicate better performance.
testMSE = loss(Mdl,XTest,YTest)
testMSE = 18.3681
Compare the predicted test set response values to the true response values. Plot the predicted miles per gallon (MPG) along the vertical axis and the true MPG along the horizontal axis. Points on the reference line indicate correct predictions. A good model produces predictions that are scattered near the line.
testPredictions = predict(Mdl,XTest); plot(YTest,testPredictions,".") hold on plot(YTest,YTest) hold off xlabel("True MPG") ylabel("Predicted MPG")
Stop Neural Network Training Early Using Validation Data
At each iteration of the training process, compute the validation loss of the neural network. Stop the training process early if the validation loss reaches a reasonable minimum.
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 validation set tblValidation
. The software reserves approximately 30% of the observations for the validation 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); validationIndices = test(c); tblTrain = tbl(trainingIndices,:); tblValidation = tbl(validationIndices,:);
Train a neural network regression model by using the training set. Specify the Systolic
column of tblTrain
as the response variable. Evaluate the model at each iteration by using the validation set. Specify to display the training information at each iteration by using the Verbose
name-value argument. By default, the training process ends early if the validation loss is greater than or equal to the minimum validation loss computed so far, six times in a row. To change the number of times the validation loss is allowed to be greater than or equal to the minimum, specify the ValidationPatience
name-value argument.
Mdl = fitrnet(tblTrain,"Systolic", ... "ValidationData",tblValidation, ... "Verbose",1);
|==========================================================================================| | Iteration | Train Loss | Gradient | Step | Iteration | Validation | Validation | | | | | | Time (sec) | Loss | Checks | |==========================================================================================| | 1| 516.021993| 3220.880047| 0.644473| 0.013629| 568.289202| 0| | 2| 313.056754| 229.931405| 0.067026| 0.007363| 304.023695| 0| | 3| 308.461807| 277.166516| 0.011122| 0.001868| 296.935608| 0| | 4| 262.492770| 844.627934| 0.143022| 0.000393| 240.559640| 0| | 5| 169.558740| 1131.714363| 0.336463| 0.000394| 152.531663| 0| | 6| 89.134368| 362.084104| 0.382677| 0.000822| 83.147478| 0| | 7| 83.309729| 994.830303| 0.199923| 0.000491| 76.634122| 0| | 8| 70.731524| 327.637362| 0.041366| 0.000415| 66.421750| 0| | 9| 66.650091| 124.369963| 0.125232| 0.000413| 65.914063| 0| | 10| 66.404753| 36.699328| 0.016768| 0.000431| 65.357335| 0| |==========================================================================================| | Iteration | Train Loss | Gradient | Step | Iteration | Validation | Validation | | | | | | Time (sec) | Loss | Checks | |==========================================================================================| | 11| 66.357143| 46.712988| 0.009405| 0.001282| 65.306106| 0| | 12| 66.268225| 54.079264| 0.007953| 0.001160| 65.234391| 0| | 13| 65.788550| 99.453225| 0.030942| 0.000469| 64.869708| 0| | 14| 64.821095| 186.344649| 0.048078| 0.000451| 64.191533| 0| | 15| 62.353896| 319.273873| 0.107160| 0.000510| 62.618374| 0| | 16| 57.836593| 447.826470| 0.184985| 0.000419| 60.087065| 0| | 17| 51.188884| 524.631067| 0.253062| 0.000429| 56.646294| 0| | 18| 41.755601| 189.072516| 0.318515| 0.000395| 49.046823| 0| | 19| 37.539854| 78.602559| 0.382284| 0.002361| 44.633562| 0| | 20| 36.845322| 151.837884| 0.211286| 0.000386| 47.291367| 1| |==========================================================================================| | Iteration | Train Loss | Gradient | Step | Iteration | Validation | Validation | | | | | | Time (sec) | Loss | Checks | |==========================================================================================| | 21| 36.218289| 62.826818| 0.142748| 0.000380| 46.139104| 2| | 22| 35.776921| 53.606315| 0.215188| 0.000382| 46.170460| 3| | 23| 35.729085| 24.400342| 0.060096| 0.002195| 45.318023| 4| | 24| 35.622031| 9.602277| 0.121153| 0.000337| 45.791861| 5| | 25| 35.573317| 10.735070| 0.126854| 0.000334| 46.062826| 6| |==========================================================================================|
Create a plot that compares the training mean squared error (MSE) and the validation MSE at each iteration. By default, fitrnet
stores the loss information inside the TrainingHistory
property of the object Mdl
. You can access this information by using dot notation.
iteration = Mdl.TrainingHistory.Iteration; trainLosses = Mdl.TrainingHistory.TrainingLoss; valLosses = Mdl.TrainingHistory.ValidationLoss; plot(iteration,trainLosses,iteration,valLosses) legend(["Training","Validation"]) xlabel("Iteration") ylabel("Mean Squared Error")
Check the iteration that corresponds to the minimum validation MSE. The final returned model Mdl
is the model trained at this iteration.
[~,minIdx] = min(valLosses); iteration(minIdx)
ans = 19
Find Good Regularization Strength for Neural Network Using Cross-Validation
Assess the cross-validation loss of neural network models with different regularization strengths, and choose the regularization strength corresponding to the best performing model.
Load the carbig
data set, which contains measurements of cars made in the 1970s and early 1980s. Create a table containing the predictor variables Acceleration
, Displacement
, and so on, as well as the response variable MPG
.
load carbig cars = table(Acceleration,Displacement,Horsepower, ... Model_Year,Origin,Weight,MPG);
Delete 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");
Create a cvpartition
object for 5-fold cross-validation. cvp
partitions the data into five folds, where each fold has roughly the same number of observations. Set the random seed to the default value for reproducibility of the partition.
rng("default") n = size(cars,1); cvp = cvpartition(n,"KFold",5);
Compute the cross-validation mean squared error (MSE) for neural network regression models with different regularization strengths. Try regularization strengths on the order of 1/n, where n is the number of observations. Specify to standardize the data before training the neural network models.
1/n
ans = 0.0026
lambda = (0:0.5:5)*1e-3; cvloss = zeros(length(lambda),1); for i = 1:length(lambda) cvMdl = fitrnet(cars,"MPG","Lambda",lambda(i), ... "CVPartition",cvp,"Standardize",true); cvloss(i) = kfoldLoss(cvMdl); end
Plot the results. Find the regularization strength corresponding to the lowest cross-validation MSE.
plot(lambda,cvloss) xlabel("Regularization Strength") ylabel("Cross-Validation Loss")
[~,idx] = min(cvloss); bestLambda = lambda(idx)
bestLambda = 0.0045
Train a neural network regression model using the bestLambda
regularization strength.
Mdl = fitrnet(cars,"MPG","Lambda",bestLambda, ... "Standardize",true)
Mdl = RegressionNeuralNetwork PredictorNames: {'Acceleration' 'Displacement' 'Horsepower' 'Model_Year' 'Origin' 'Weight'} ResponseName: 'MPG' CategoricalPredictors: 5 ResponseTransform: 'none' NumObservations: 392 LayerSizes: 10 Activations: 'relu' OutputLayerActivation: 'none' Solver: 'LBFGS' ConvergenceInfo: [1×1 struct] TrainingHistory: [761×7 table] Properties, Methods
Minimize Cross-Validation Error in Neural Network
Create a neural network with low error by using the OptimizeHyperparameters
argument. This argument causes fitrnet
to minimize cross-validation loss over some problem hyperparameters by using Bayesian optimization.
Load the carbig
data set, which contains measurements of cars made in the 1970s and early 1980s. Create a table containing the predictor variables Acceleration
, Displacement
, and so on, as well as the response variable MPG
.
load carbig cars = table(Acceleration,Displacement,Horsepower, ... Model_Year,Origin,Weight,MPG);
Delete 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 80% of the observations to train a neural network model, and 20% of the observations to test the performance of the trained model on new data. Use cvpartition
to partition the data.
rng("default") % For reproducibility of the data partition c = cvpartition(height(cars),"Holdout",0.20); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
Train a regression neural network using the OptimizeHyperparameters
argument set to "auto"
. For reproducibility, set the AcquisitionFunctionName
to "expected-improvement-plus"
in a HyperparameterOptimizationOptions
structure. fitrnet
performs Bayesian optimization by default. To use grid search or random search, set the Optimizer
field in HyperparameterOptimizationOptions
.
rng("default") % For reproducibility Mdl = fitrnet(carsTrain,"MPG","OptimizeHyperparameters","auto", ... "HyperparameterOptimizationOptions",struct("AcquisitionFunctionName","expected-improvement-plus"))
|============================================================================================================================================| | Iter | Eval | Objective: | Objective | BestSoFar | BestSoFar | Activations | Standardize | Lambda | LayerSizes | | | result | log(1+loss) | runtime | (observed) | (estim.) | | | | | |============================================================================================================================================| | 1 | Best | 2.223 | 9.231 | 2.223 | 2.223 | relu | true | 3.841 | [101 47 15] | | 2 | Accept | 3.0797 | 6.4178 | 2.223 | 2.2571 | sigmoid | false | 7.5401e-07 | [100 17] | | 3 | Best | 2.1171 | 2.4398 | 2.1171 | 2.1312 | relu | true | 0.01569 | 15 | | 4 | Accept | 2.5142 | 4.2068 | 2.1171 | 2.1326 | none | true | 0.00016461 | [ 2 145 8] | | 5 | Accept | 3.0246 | 0.26994 | 2.1171 | 2.1172 | relu | true | 5.4264e-08 | 1 | | 6 | Accept | 2.9859 | 0.77249 | 2.1171 | 2.171 | relu | true | 0.1243 | [ 5 1] | | 7 | Accept | 2.14 | 2.5549 | 2.1171 | 2.1173 | relu | true | 0.0082696 | 17 | | 8 | Accept | 2.7596 | 0.41156 | 2.1171 | 2.1173 | relu | true | 5.8567 | 72 | | 9 | Accept | 3.0702 | 6.3673 | 2.1171 | 2.1173 | relu | true | 4.4611e-07 | [ 77 24 12] | | 10 | Accept | 2.2126 | 1.8954 | 2.1171 | 2.1177 | relu | true | 4.1722e-07 | 9 | | 11 | Accept | 2.9998 | 16.958 | 2.1171 | 2.1177 | relu | true | 0.00088575 | [250 47 63] | | 12 | Accept | 3.3504 | 11.524 | 2.1171 | 2.1173 | relu | true | 1.2716e-06 | [103 55 15] | | 13 | Accept | 2.223 | 1.7197 | 2.1171 | 2.1174 | relu | true | 0.0003368 | 10 | | 14 | Accept | 6.4098 | 0.22799 | 2.1171 | 2.1301 | relu | true | 251.71 | [ 67 34 275] | | 15 | Accept | 6.412 | 0.12626 | 2.1171 | 2.1175 | relu | true | 298.04 | [ 30 23 10] | | 16 | Accept | 2.1882 | 1.6043 | 2.1171 | 2.1176 | relu | true | 5.2998e-05 | 6 | | 17 | Accept | 2.5141 | 0.46234 | 2.1171 | 2.1176 | none | true | 0.0031007 | 4 | | 18 | Accept | 2.5139 | 2.2299 | 2.1171 | 2.1176 | none | true | 0.07401 | [ 33 16 83] | | 19 | Accept | 2.5756 | 0.10945 | 2.1171 | 2.1173 | none | true | 1.6796 | 2 | | 20 | Best | 2.0906 | 8.1833 | 2.0906 | 2.0906 | relu | true | 0.58373 | [ 13 58 65] | |============================================================================================================================================| | Iter | Eval | Objective: | Objective | BestSoFar | BestSoFar | Activations | Standardize | Lambda | LayerSizes | | | result | log(1+loss) | runtime | (observed) | (estim.) | | | | | |============================================================================================================================================| | 21 | Accept | 2.4488 | 2.5839 | 2.0906 | 2.091 | relu | true | 3.4514e-06 | 26 | | 22 | Accept | 2.5142 | 3.9131 | 2.0906 | 2.091 | none | true | 3.9367e-06 | 255 | | 23 | Accept | 2.5142 | 0.21115 | 2.0906 | 2.0909 | none | true | 9.1909e-08 | [ 27 12 14] | | 24 | Accept | 6.3852 | 0.32065 | 2.0906 | 2.0908 | none | true | 91.409 | [ 27 193 71] | | 25 | Accept | 2.5312 | 15.695 | 2.0906 | 2.0908 | sigmoid | false | 0.00062 | [165 66] | | 26 | Accept | 2.588 | 4.0838 | 2.0906 | 2.0908 | sigmoid | false | 0.035987 | 100 | | 27 | Accept | 3.9253 | 6.7469 | 2.0906 | 2.0908 | sigmoid | false | 3.0045 | [ 5 296] | | 28 | Accept | 2.1903 | 8.4032 | 2.0906 | 2.0911 | relu | true | 1.1661 | [ 3 300 232] | | 29 | Accept | 2.5142 | 2.5771 | 2.0906 | 2.0912 | none | true | 1.636e-06 | [ 1 294 27] | | 30 | Accept | 2.1336 | 6.7976 | 2.0906 | 2.0911 | relu | true | 0.039606 | [ 4 299] | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 138.7963 seconds Total objective function evaluation time: 129.0442 Best observed feasible point: Activations Standardize Lambda LayerSizes ___________ ___________ _______ ______________ relu true 0.58373 13 58 65 Observed objective function value = 2.0906 Estimated objective function value = 2.0911 Function evaluation time = 8.1833 Best estimated feasible point (according to models): Activations Standardize Lambda LayerSizes ___________ ___________ _______ ______________ relu true 0.58373 13 58 65 Estimated objective function value = 2.0911 Estimated function evaluation time = 8.1846
Mdl = RegressionNeuralNetwork PredictorNames: {'Acceleration' 'Displacement' 'Horsepower' 'Model_Year' 'Origin' 'Weight'} ResponseName: 'MPG' CategoricalPredictors: 5 ResponseTransform: 'none' NumObservations: 314 HyperparameterOptimizationResults: [1×1 BayesianOptimization] LayerSizes: [13 58 65] Activations: 'relu' OutputLayerActivation: 'none' Solver: 'LBFGS' ConvergenceInfo: [1×1 struct] TrainingHistory: [1000×7 table] Properties, Methods
Find the mean squared error of the resulting model on the test data set.
testMSE = loss(Mdl,carsTest,"MPG")
testMSE = 7.3273
Custom Hyperparameter Optimization in Neural Network
Create a neural network with low error by using the OptimizeHyperparameters
argument. This argument causes fitrnet
to search for hyperparameters that give a model with low cross-validation error. Use the hyperparameters
function to specify larger-than-default values for the number of layers used and the layer size range.
Load the carbig
data set, which contains measurements of cars made in the 1970s and early 1980s. Create a table containing the predictor variables Acceleration
, Displacement
, and so on, as well as the response variable MPG
.
load carbig cars = table(Acceleration,Displacement,Horsepower, ... Model_Year,Origin,Weight,MPG);
Delete 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 80% of the observations to train a neural network model, and 20% of the observations to test the performance of the trained model on new data. Use cvpartition
to partition the data.
rng("default") % For reproducibility of the data partition c = cvpartition(height(cars),"Holdout",0.20); trainingIdx = training(c); % Training set indices carsTrain = cars(trainingIdx,:); testIdx = test(c); % Test set indices carsTest = cars(testIdx,:);
List the hyperparameters available for this problem of fitting the MPG
response.
params = hyperparameters("fitrnet",carsTrain,"MPG"); for ii = 1:length(params) disp(ii);disp(params(ii)) end
1 optimizableVariable with properties: Name: 'NumLayers' Range: [1 3] Type: 'integer' Transform: 'none' Optimize: 1 2 optimizableVariable with properties: Name: 'Activations' Range: {'relu' 'tanh' 'sigmoid' 'none'} Type: 'categorical' Transform: 'none' Optimize: 1 3 optimizableVariable with properties: Name: 'Standardize' Range: {'true' 'false'} Type: 'categorical' Transform: 'none' Optimize: 1 4 optimizableVariable with properties: Name: 'Lambda' Range: [3.1847e-08 318.4713] Type: 'real' Transform: 'log' Optimize: 1 5 optimizableVariable with properties: Name: 'LayerWeightsInitializer' Range: {'glorot' 'he'} Type: 'categorical' Transform: 'none' Optimize: 0 6 optimizableVariable with properties: Name: 'LayerBiasesInitializer' Range: {'zeros' 'ones'} Type: 'categorical' Transform: 'none' Optimize: 0 7 optimizableVariable with properties: Name: 'Layer_1_Size' Range: [1 300] Type: 'integer' Transform: 'log' Optimize: 1 8 optimizableVariable with properties: Name: 'Layer_2_Size' Range: [1 300] Type: 'integer' Transform: 'log' Optimize: 1 9 optimizableVariable with properties: Name: 'Layer_3_Size' Range: [1 300] Type: 'integer' Transform: 'log' Optimize: 1 10 optimizableVariable with properties: Name: 'Layer_4_Size' Range: [1 300] Type: 'integer' Transform: 'log' Optimize: 0 11 optimizableVariable with properties: Name: 'Layer_5_Size' Range: [1 300] Type: 'integer' Transform: 'log' Optimize: 0
To try more layers than the default of 1 through 3, set the range of NumLayers
(optimizable variable 1) to its maximum allowable size, [1 5]
. Also, set Layer_4_Size
and Layer_5_Size
(optimizable variables 10 and 11, respectively) to be optimized.
params(1).Range = [1 5]; params(10).Optimize = true; params(11).Optimize = true;
Set the range of all layer sizes (optimizable variables 7 through 11) to [1 400]
instead of the default [1 300]
.
for ii = 7:11 params(ii).Range = [1 400]; end
Train a regression neural network using the OptimizeHyperparameters
argument set to params
. For reproducibility, set the AcquisitionFunctionName
to "expected-improvement-plus"
in a HyperparameterOptimizationOptions
structure. To attempt to get a better solution, set the number of optimization steps to 60 instead of the default 30.
rng("default") % For reproducibility Mdl = fitrnet(carsTrain,"MPG","OptimizeHyperparameters",params, ... "HyperparameterOptimizationOptions", ... struct("AcquisitionFunctionName","expected-improvement-plus", ... "MaxObjectiveEvaluations",60))
|============================================================================================================================================| | Iter | Eval | Objective: | Objective | BestSoFar | BestSoFar | Activations | Standardize | Lambda | LayerSizes | | | result | log(1+loss) | runtime | (observed) | (estim.) | | | | | |============================================================================================================================================| | 1 | Best | 4.9294 | 0.35241 | 4.9294 | 4.9294 | sigmoid | false | 70.242 | [ 3 22 223] | | 2 | Best | 2.211 | 3.976 | 2.211 | 2.3191 | relu | true | 0.089397 | [ 2 95] | | 3 | Accept | 2.7225 | 23.043 | 2.211 | 2.2929 | sigmoid | false | 2.5899e-07 | [303 60 59] | | 4 | Accept | 3.5246 | 4.4994 | 2.211 | 2.2883 | relu | false | 5.1748e-05 | [102 5 15 1] | | 5 | Accept | 2.2357 | 3.2875 | 2.211 | 2.2164 | relu | true | 0.095678 | [ 2 68] | | 6 | Accept | 3.0174 | 1.3174 | 2.211 | 2.2144 | relu | true | 0.0031767 | [ 2 1] | | 7 | Accept | 2.3385 | 0.64635 | 2.211 | 2.2199 | relu | true | 0.043248 | 2 | | 8 | Accept | 4.8512 | 0.52613 | 2.211 | 2.2199 | relu | true | 3.387 | [ 2 23 5 1] | | 9 | Accept | 2.4583 | 0.16388 | 2.211 | 2.2236 | relu | true | 1.0849 | [ 1 10] | | 10 | Accept | 3.1863 | 3.8647 | 2.211 | 2.2237 | relu | true | 0.061861 | [ 63 1 1 112] | | 11 | Accept | 3.8592 | 3.3615 | 2.211 | 2.2235 | relu | true | 0.20233 | [ 2 45 1 4 59] | | 12 | Accept | 3.3752 | 3.4719 | 2.211 | 2.2111 | relu | true | 1.556e-05 | [ 4 18 1 104] | | 13 | Accept | 6.4116 | 0.15784 | 2.211 | 2.2198 | relu | true | 287.34 | [ 34 196] | | 14 | Accept | 2.3537 | 0.21589 | 2.211 | 2.2104 | relu | true | 5.3986 | [ 2 12] | | 15 | Accept | 3.1122 | 0.077105 | 2.211 | 2.2109 | relu | true | 7.2543 | 1 | | 16 | Accept | 6.4092 | 0.11676 | 2.211 | 2.2142 | relu | true | 241.19 | [ 1 389] | | 17 | Best | 2.1517 | 0.69926 | 2.1517 | 2.1523 | relu | true | 0.24096 | 4 | | 18 | Best | 2.1273 | 0.87139 | 2.1273 | 2.1274 | relu | true | 0.11077 | 5 | | 19 | Accept | 4.1318 | 0.14418 | 2.1273 | 2.1274 | sigmoid | false | 4.8026e-06 | [ 12 106 59] | | 20 | Accept | 2.2859 | 0.61843 | 2.1273 | 2.1269 | relu | true | 8.3707 | [ 2 9 1 5 9] | |============================================================================================================================================| | Iter | Eval | Objective: | Objective | BestSoFar | BestSoFar | Activations | Standardize | Lambda | LayerSizes | | | result | log(1+loss) | runtime | (observed) | (estim.) | | | | | |============================================================================================================================================| | 21 | Accept | 2.1981 | 11.621 | 2.1273 | 2.1265 | relu | true | 4.0719 | [203 124 1 62] | | 22 | Accept | 4.1318 | 0.117 | 2.1273 | 2.1269 | sigmoid | false | 5.7744e-08 | [317 4 60 1] | | 23 | Accept | 2.9406 | 2.6457 | 2.1273 | 2.1268 | relu | true | 7.2868 | [ 23 7 1 373] | | 24 | Accept | 5.4267 | 0.15109 | 2.1273 | 2.1276 | relu | true | 3.4444 | [ 1 253 1] | | 25 | Accept | 3.5359 | 1.7515 | 2.1273 | 2.1276 | relu | true | 36.471 | [ 51 3 204 71] | | 26 | Accept | 4.1542 | 1.3619 | 2.1273 | 2.1276 | relu | true | 1.2334 | [ 5 4 1 95] | | 27 | Accept | 2.3033 | 15.761 | 2.1273 | 2.1276 | relu | true | 0.028889 | [ 42 348] | | 28 | Accept | 4.1318 | 0.093199 | 2.1273 | 2.1276 | sigmoid | false | 5.9314e-08 | [109 9] | | 29 | Accept | 3.0644 | 18.95 | 2.1273 | 2.1276 | sigmoid | false | 3.2982e-08 | [388 3 331] | | 30 | Accept | 2.8076 | 4.1115 | 2.1273 | 2.1277 | relu | true | 0.00077627 | 183 | | 31 | Accept | 3.3041 | 3.4421 | 2.1273 | 2.1277 | relu | true | 2.1595e-05 | 116 | | 32 | Accept | 3.1379 | 11.325 | 2.1273 | 2.1276 | relu | true | 2.2732e-05 | [187 41] | | 33 | Accept | 3.3071 | 6.2584 | 2.1273 | 2.1277 | relu | true | 2.7221e-07 | [120 23] | | 34 | Accept | 2.2511 | 4.5188 | 2.1273 | 2.1277 | relu | true | 2.6888 | [ 2 104 142 60] | | 35 | Accept | 2.3491 | 7.7419 | 2.1273 | 2.1277 | relu | true | 4.3755 | [ 1 322 277 53] | | 36 | Accept | 6.3658 | 0.2106 | 2.1273 | 2.129 | relu | true | 60.596 | [ 4 17 12 47] | | 37 | Accept | 2.1727 | 4.9758 | 2.1273 | 2.1291 | relu | true | 0.0059602 | [ 2 110] | | 38 | Accept | 2.5005 | 28.335 | 2.1273 | 2.1288 | relu | true | 0.052893 | [252 99 208 55] | | 39 | Accept | 2.2474 | 31.45 | 2.1273 | 2.1301 | relu | true | 6.086 | [356 136 307 70] | | 40 | Best | 2.0745 | 37.552 | 2.0745 | 2.0746 | relu | true | 0.55888 | [288 115 213 120] | |============================================================================================================================================| | Iter | Eval | Objective: | Objective | BestSoFar | BestSoFar | Activations | Standardize | Lambda | LayerSizes | | | result | log(1+loss) | runtime | (observed) | (estim.) | | | | | |============================================================================================================================================| | 41 | Accept | 2.0896 | 26.315 | 2.0745 | 2.0747 | relu | true | 0.98992 | [270 74 258 28] | | 42 | Accept | 4.1421 | 0.53203 | 2.0745 | 2.0746 | relu | true | 13.353 | [ 4 376 1 149] | | 43 | Accept | 2.6447 | 5.5647 | 2.0745 | 2.0746 | relu | true | 0.026383 | [ 18 118 1 23] | | 44 | Accept | 2.4817 | 27.009 | 2.0745 | 2.0747 | relu | true | 0.013213 | [389 175] | | 45 | Accept | 2.3857 | 6.6975 | 2.0745 | 2.0746 | relu | true | 0.0012278 | [ 4 386] | | 46 | Accept | 2.0888 | 6.0115 | 2.0745 | 2.0746 | relu | true | 0.12715 | 354 | | 47 | Accept | 4.0279 | 1.866 | 2.0745 | 2.0747 | relu | true | 3.1997 | [ 8 46 1 7] | | 48 | Accept | 2.1107 | 3.9274 | 2.0745 | 2.0747 | relu | true | 0.87573 | [ 75 3] | | 49 | Accept | 2.8679 | 17.581 | 2.0745 | 2.0747 | relu | true | 0.014349 | [382 19 2 217] | | 50 | Accept | 2.12 | 31.823 | 2.0745 | 2.0748 | relu | true | 1.4981 | [ 9 250 205 316] | | 51 | Accept | 2.0956 | 9.3003 | 2.0745 | 2.0749 | relu | true | 0.50519 | [ 13 25 234] | | 52 | Accept | 2.0788 | 20.963 | 2.0745 | 2.0748 | relu | true | 0.20245 | [ 30 340 72] | | 53 | Accept | 2.0793 | 15.073 | 2.0745 | 2.0749 | relu | true | 0.30508 | [230 27 157] | | 54 | Best | 2.0571 | 14.353 | 2.0571 | 2.0572 | relu | true | 0.40191 | [ 58 58 83 4] | | 55 | Accept | 2.2477 | 5.5372 | 2.0571 | 2.0572 | relu | true | 0.056099 | [ 8 2 166] | | 56 | Accept | 2.2329 | 9.6228 | 2.0571 | 2.0571 | relu | true | 0.15146 | [ 1 46 169 9] | | 57 | Accept | 2.2506 | 11.931 | 2.0571 | 2.0571 | relu | true | 0.0068432 | [ 2 263 19] | | 58 | Accept | 2.2439 | 6.1584 | 2.0571 | 2.0572 | relu | true | 0.0037586 | [ 2 191 2] | | 59 | Accept | 6.3612 | 0.15672 | 2.0571 | 2.0572 | relu | true | 56.064 | [ 19 2 2 1 9] | | 60 | Accept | 2.7839 | 5.6539 | 2.0571 | 2.0573 | relu | true | 0.011315 | [ 18 33 49] | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 60 reached. Total function evaluations: 60 Total elapsed time: 494.8036 seconds Total objective function evaluation time: 469.8626 Best observed feasible point: Activations Standardize Lambda LayerSizes ___________ ___________ _______ ____________________ relu true 0.40191 58 58 83 4 Observed objective function value = 2.0571 Estimated objective function value = 2.0573 Function evaluation time = 14.3527 Best estimated feasible point (according to models): Activations Standardize Lambda LayerSizes ___________ ___________ _______ ____________________ relu true 0.40191 58 58 83 4 Estimated objective function value = 2.0573 Estimated function evaluation time = 14.3565
Mdl = RegressionNeuralNetwork PredictorNames: {'Acceleration' 'Displacement' 'Horsepower' 'Model_Year' 'Origin' 'Weight'} ResponseName: 'MPG' CategoricalPredictors: 5 ResponseTransform: 'none' NumObservations: 314 HyperparameterOptimizationResults: [1×1 BayesianOptimization] LayerSizes: [58 58 83 4] Activations: 'relu' OutputLayerActivation: 'none' Solver: 'LBFGS' ConvergenceInfo: [1×1 struct] TrainingHistory: [1000×7 table] Properties, Methods
Find the mean squared error of the resulting model on the test data set.
testMSE = loss(Mdl,carsTest,"MPG")
testMSE = 7.1939
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
Tbl
— Sample data
table
Sample data used to train the model, specified as a table. Each row of
Tbl
corresponds to one observation, and each column corresponds
to one predictor variable. Multicolumn variables and cell arrays other than cell arrays
of character vectors are not allowed.
Optionally,
Tbl
can contain columns for the response variables and a column for the observation weights. Each response variable and the weight values must be numeric vectors.You must specify the response variables in
Tbl
by usingResponseVarName
orformula
and specify the observation weights inTbl
by usingWeights
.When you specify the response variables by using
ResponseVarName
,fitrnet
uses the remaining variables as predictors. To use a subset of the remaining variables inTbl
as predictors, specify predictor variables by usingPredictorNames
.When you define a model specification by using
formula
,fitrnet
uses a subset of the variables inTbl
as predictor variables and response variables, as specified informula
.
If
Tbl
does not contain the response variables, then specify them by usingY
. IfY
is a vector, then the length of the response variable and the number of rows inTbl
must be equal. IfY
is a matrix, thenY
andTbl
must have the same number of rows. To use a subset of the variables inTbl
as predictors, specify predictor variables by usingPredictorNames
.
Data Types: table
ResponseVarName
— Response variable names
names of variables in Tbl
Response variable names, specified as the names of variables in
Tbl
. Each response variable must be a numeric vector.
You must specify ResponseVarName
as a character vector, string
array, or cell array of character vectors. For example, if Tbl
stores
the response variable Y
as Tbl.Y
, then specify it
as "Y"
. Otherwise, the software treats the Y
column of Tbl
as a predictor when training the model.
Data Types: char
| string
| cell
formula
— Explanatory model of response variables and subset of predictor variables
character vector | string scalar
Explanatory model of the response variables and a subset of the predictor variables,
specified as a character vector or string scalar in the form
"Y1,Y2~x1+x2+x3"
. In this form, Y1
and
Y2
represent the response variables, and x1
,
x2
, and x3
represent the predictor
variables.
To specify a subset of variables in Tbl
as predictors for
training the model, use a formula. If you specify a formula, then the software does not
use any variables in Tbl
that do not appear in
formula
, except for observation weights (if specified).
The variable names in the formula must be both variable names in Tbl
(Tbl.Properties.VariableNames
) and valid MATLAB® identifiers. You can verify the variable names in Tbl
by
using the isvarname
function. If the variable names
are not valid, then you can convert them by using the matlab.lang.makeValidName
function.
Data Types: char
| string
Y
— Response data
numeric vector | numeric matrix | numeric table
Response data, specified as a numeric vector, matrix, or table.
To use one response variable, specify
Y
as a vector. The length ofY
must be equal to the number of observations inX
orTbl
.To use multiple response variables, specify
Y
as a matrix or table, where each column corresponds to a response variable.Y
and the predictor data (X
orTbl
) must have the same number of rows.
Data Types: single
| double
| table
X
— Predictor data
numeric matrix
Predictor data used to train the model, specified as a numeric matrix.
By default, the software treats each row of X
as one
observation, and each column as one predictor.
X
and Y
must have the same number of
observations.
To specify the names of the predictors in the order of their appearance in
X
, use the PredictorNames
name-value
argument.
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.
Data Types: single
| double
Note
When training a model with one response variable, the software treats
NaN
, empty character vector (''
), empty string
(""
), <missing>
, and
<undefined>
elements as missing values, and removes observations
with any of these characteristics:
Missing value in the response (for example,
Y
orValidationData
{2}
)At least one missing value in a predictor observation (for example, row in
X
orValidationData{1}
)NaN
value or0
weight (for example, value inWeights
orValidationData{3}
)
When you train a model with multiple response variables, remove missing values from the
data arguments before passing them to fitrnet
.
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: fitrnet(X,Y,LayerSizes=[10 10],Activations=["relu","tanh"])
specifies to create a neural network with two fully connected layers, each with 10 outputs.
The first layer uses a rectified linear unit (ReLU) activation function, and the second uses
a hyperbolic tangent activation function.
LayerSizes
— Sizes of fully connected layers
10
(default) | positive integer vector
Sizes of the fully connected layers in the neural network model, specified as a positive integer vector. The ith element of LayerSizes
is the number of outputs in the ith fully connected layer of the neural network model.
LayerSizes
does not include the size of the final fully connected layer. For more information, see Neural Network Structure.
Example: LayerSizes=[100 25 10]
Activations
— Activation functions for fully connected layers
"relu"
(default) | "tanh"
| "sigmoid"
| "none"
| string array | cell array of character vectors
Activation functions for the fully connected layers of the neural network model, specified as a character vector, string scalar, string array, or cell array of character vectors with values from this table.
Value | Description |
---|---|
"relu" | Rectified linear unit (ReLU) function — Performs a threshold operation on each element of the input, where any value less than zero is set to zero, that is, |
"tanh" | Hyperbolic tangent (tanh) function — Applies the |
"sigmoid" | Sigmoid function — Performs the following operation on each input element: |
"none" | Identity function — Returns each input element without performing any transformation, that is, f(x) = x |
If you specify one activation function only, then
Activations
is the activation function for every fully connected layer of the neural network model, excluding the final fully connected layer (see Neural Network Structure).If you specify an array of activation functions, then the ith element of
Activations
is the activation function for the ith layer of the neural network model.
Example: Activations="sigmoid"
LayerWeightsInitializer
— Function to initialize fully connected layer weights
"glorot"
(default) | "he"
Function to initialize the fully connected layer weights, specified as
"glorot"
or "he"
.
Value | Description |
---|---|
"glorot" | Initialize the weights with the Glorot initializer [1]
(also known as the Xavier initializer). For each layer, the Glorot
initializer independently samples from a uniform distribution with
zero mean and variance 2/(I+O) , where
I is the input size and O
is the output size for the layer. |
"he" | Initialize the weights with the He initializer [2].
For each layer, the He initializer samples from a normal
distribution with zero mean and variance 2/I ,
where I is the input size for the layer. |
Example: LayerWeightsInitializer="he"
Data Types: char
| string
LayerBiasesInitializer
— Type of initial fully connected layer biases
"zeros"
(default) | "ones"
Type of initial fully connected layer biases, specified as "zeros"
or
"ones"
.
If you specify the value
"zeros"
, then each fully connected layer has an initial bias of 0.If you specify the value
"ones"
, then each fully connected layer has an initial bias of 1.
Example: LayerBiasesInitializer="ones"
Data Types: char
| string
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.
Example: ObservationsIn="columns"
Data Types: char
| string
Lambda
— Regularization term strength
0
(default) | nonnegative scalar
Regularization term strength, specified as a nonnegative scalar. The software composes the objective function for minimization from the mean squared error (MSE) loss function and the ridge (L2) penalty term.
Example: Lambda=1e-4
Data Types: single
| double
Standardize
— Flag to standardize predictor data
false
or 0
(default) | true
or 1
Flag to standardize the predictor data, specified as a numeric or logical 0
(false
) or 1
(true
). If you
set Standardize
to true
, then the software
centers and scales each numeric predictor variable by the corresponding column mean and
standard deviation. The software does not standardize categorical predictors.
Example: Standardize=true
Data Types: single
| double
| logical
StandardizeResponses
— Flag to standardize response data
false
or 0
(default) | true
or 1
Since R2024b
Flag to standardize the response data before fitting the model, specified as a
numeric or logical 0
(false
) or
1
(true
). If you set
StandardizeResponses
to true
, then the
software centers and scales each response variable by the corresponding column mean
and standard deviation.
Example: StandardizeResponses=true
Data Types: single
| double
| logical
Verbose
— Verbosity level
0
(default) | 1
Verbosity level, specified as 0
or 1
. The
Verbose
name-value argument controls the amount of diagnostic
information that fitrnet
displays at the command
line.
Value | Description |
---|---|
0 | fitrnet does not display diagnostic
information. |
1 | fitrnet periodically displays diagnostic
information. |
By default, StoreHistory
is set to
true
and fitrnet
stores the diagnostic
information inside of Mdl
. Use
Mdl.TrainingHistory
to access the diagnostic information.
Example: Verbose=1
Data Types: single
| double
VerboseFrequency
— Frequency of verbose printing
1
(default) | positive integer scalar
Frequency of verbose printing, which is the number of iterations between printing diagnostic information at the command line, specified as a positive integer scalar. A value of 1 indicates to print diagnostic information at every iteration.
Note
To use this name-value argument, you must set
Verbose
to
1
.
Example: VerboseFrequency=5
Data Types: single
| double
StoreHistory
— Flag to store training history
true
or 1
(default) | false
or 0
Flag to store the training history, specified as a numeric or logical
0
(false
) or 1
(true
). If StoreHistory
is set to
true
, then the software stores diagnostic information inside of
Mdl
, which you can access by using
Mdl.TrainingHistory
.
Example: StoreHistory=false
Data Types: single
| double
| logical
InitialStepSize
— Initial step size
[]
(default) | positive scalar | "auto"
Initial step size, specified as a positive scalar or "auto"
. By default,
fitrnet
does not use the initial step size to determine the
initial Hessian approximation used in training the model (see Training Solver). However, if you
specify an initial step size , then the initial inverse-Hessian approximation is . is the initial gradient vector, and is the identity matrix.
To have fitrnet
determine an initial step size automatically, specify the
value as "auto"
. In this case, the function determines the initial
step size by using . is the initial step vector, and is the vector of unconstrained initial weights and biases.
Example: InitialStepSize="auto"
Data Types: single
| double
| char
| string
IterationLimit
— Maximum number of training iterations
1e3
(default) | positive integer scalar
Maximum number of training iterations, specified as a positive integer scalar.
The software returns a trained model regardless of whether the training routine
successfully converges. Mdl.ConvergenceInfo
contains convergence
information.
Example: IterationLimit=1e8
Data Types: single
| double
GradientTolerance
— Relative gradient tolerance
1e-6
(default) | nonnegative scalar
Relative gradient tolerance, specified as a nonnegative scalar.
Let be the loss function at training iteration t, be the gradient of the loss function with respect to the weights and biases at iteration t, and be the gradient of the loss function at an initial point. If , where , then the training process terminates.
Example: GradientTolerance=1e-5
Data Types: single
| double
LossTolerance
— Loss tolerance
1e-6
(default) | nonnegative scalar
Loss tolerance, specified as a nonnegative scalar.
If the function loss at some iteration is smaller than LossTolerance
, then the training process terminates.
Example: LossTolerance=1e-8
Data Types: single
| double
StepTolerance
— Step size tolerance
1e-6
(default) | nonnegative scalar
Step size tolerance, specified as a nonnegative scalar.
If the step size at some iteration is smaller than StepTolerance
, then the training process terminates.
Example: StepTolerance=1e-4
Data Types: single
| double
ValidationData
— Validation data for training convergence detection
cell array | table
Validation data for training convergence detection, specified as a cell array or a table.
During the training process, the software periodically estimates the validation loss by using
ValidationData
. If the validation loss increases more than
ValidationPatience
times consecutively, then the software
terminates the training.
You can specify ValidationData
as a table if you use a table Tbl
of predictor data that contains the response variable. In this case, ValidationData
must contain the same predictors and response contained in Tbl
. The software does not apply weights to observations, even if Tbl
contains a vector of weights. To specify weights, you must specify ValidationData
as a cell array.
If you specify ValidationData
as a cell array, then it must have the following format:
ValidationData{1}
must have the same data type and orientation as the predictor data. That is, if you use a predictor matrixX
, thenValidationData{1}
must be an m-by-p or p-by-m matrix of predictor data that has the same orientation asX
. The predictor variables in the training dataX
andValidationData{1}
must correspond. Similarly, if you use a predictor tableTbl
of predictor data, thenValidationData{1}
must be a table containing the same predictor variables contained inTbl
. The number of observations inValidationData{1}
and the predictor data can vary.ValidationData{2}
must match the data type and format of the response variable, eitherY
orResponseVarName
. IfValidationData{2}
is an array of responses, then it must have the same number of elements as the number of observations inValidationData{1}
. IfValidationData{1}
is a table, thenValidationData{2}
can be the name of the response variable in the table. If you want to use the sameResponseVarName
orformula
, you can specifyValidationData{2}
as[]
.Optionally, you can specify
ValidationData{3}
as an m-dimensional numeric vector of observation weights or the name of a variable in the tableValidationData{1}
that contains observation weights. The software normalizes the weights with the validation data so that they sum to 1.
If you specify ValidationData
and want to display the validation loss at the command line, set Verbose
to 1
.
Data Types: table
| cell
ValidationFrequency
— Number of iterations between validation evaluations
1
(default) | positive integer scalar
Number of iterations between validation evaluations, specified as a positive integer scalar. A value of 1 indicates to evaluate validation metrics at every iteration.
Note
To use this name-value argument, you must specify ValidationData
.
Example: ValidationFrequency=5
Data Types: single
| double
ValidationPatience
— Stopping condition for validation evaluations
6
(default) | nonnegative integer scalar
Stopping condition for validation evaluations, specified as a nonnegative integer
scalar. Training stops if the validation loss is greater than or equal to the minimum
validation loss computed so far, ValidationPatience
times in a row.
You can check the Mdl.TrainingHistory
table to see the running
total of times that the validation loss is greater than or equal to the minimum
(Validation Checks
).
Example: ValidationPatience=10
Data Types: single
| double
Note
Validation data options (ValidationData
,
ValidationFrequency
, and ValidationPatience
)
are not supported for multiresponse regression.
CategoricalPredictors
— Categorical predictors list
vector of positive integers | logical vector | character matrix | string array | cell array of character vectors | "all"
Categorical predictors list, specified as one of the values in this table. The descriptions assume that the predictor data has observations in rows and predictors in columns.
Value | Description |
---|---|
Vector of positive integers |
Each entry in the vector is an index value indicating that the corresponding predictor is
categorical. The index values are between 1 and If |
Logical vector |
A |
Character matrix | Each row of the matrix is the name of a predictor variable. The names must match the entries in PredictorNames . Pad the names with extra blanks so each row of the character matrix has the same length. |
String array or cell array of character vectors | Each element in the array is the name of a predictor variable. The names must match the entries in PredictorNames . |
"all" | All predictors are categorical. |
By default, if the
predictor data is in a table (Tbl
), fitrnet
assumes that a variable is categorical if it is a logical vector, categorical vector, character
array, string array, or cell array of character vectors. If the predictor data is a matrix
(X
), fitrnet
assumes that all predictors are
continuous. To identify any other predictors as categorical predictors, specify them by using
the CategoricalPredictors
name-value argument.
For the identified categorical predictors, fitrnet
creates
dummy variables using two different schemes, depending on whether a categorical variable
is unordered or ordered. For an unordered categorical variable,
fitrnet
creates one dummy variable for each level of the
categorical variable. For an ordered categorical variable,
fitrnet
creates one less dummy variable than the number of
categories. For details, see Automatic Creation of Dummy Variables.
Example: CategoricalPredictors="all"
Data Types: single
| double
| logical
| char
| string
| cell
PredictorNames
— Predictor variable names
string array of unique names | cell array of unique character vectors
Predictor variable names, specified as a string array of unique names or cell
array of unique character vectors. The functionality of
PredictorNames
depends on the way you supply the training data.
If you supply
X
andY
, then you can usePredictorNames
to assign names to the predictor variables inX
.The order of the names in
PredictorNames
must correspond to the predictor order inX
. Assuming thatX
has the default orientation, with observations in rows and predictors in columns,PredictorNames{1}
is the name ofX(:,1)
,PredictorNames{2}
is the name ofX(:,2)
, and so on. Also,size(X,2)
andnumel(PredictorNames)
must be equal.By default,
PredictorNames
is{'x1','x2',...}
.
If you supply
Tbl
, then you can usePredictorNames
to choose which predictor variables to use in training. That is,fitrnet
uses only the variables inPredictorNames
as predictors during training.PredictorNames
must be a subset ofTbl.Properties.VariableNames
and cannot include the name of any response variable.By default,
PredictorNames
contains the names of all predictor variables.A good practice is to specify the predictors for training using either
PredictorNames
orformula
, but not both.
Example: PredictorNames=["SepalLength","SepalWidth","PetalLength","PetalWidth"]
Data Types: string
| cell
ResponseName
— Response variable names
character vector | string array | cell array of character vectors
Response variable names, specified as a character vector, string array, or cell array of character vectors.
If you supply
Y
, then you can useResponseName
to specify names for the response variables.If you supply
ResponseVarName
orformula
, then you cannot useResponseName
.
Example: ResponseName="Response"
Example: ResponseName=["Response1","Response2"]
Data Types: char
| string
| cell
ResponseTransform
— Function for transforming raw response values
"none"
(default) | function handle | function name
Function for transforming raw response values, specified as a function handle or
function name. The default is "none"
, which means
@(y)y
, or no transformation. The function must accept the
original response values and return an output of the same size (the transformed
response values).
Example: Suppose you create a function handle that applies an exponential
transformation to an input vector by using myfunction = @(y)exp(y)
.
Then, you can specify the response transformation as
ResponseTransform=myfunction
.
Data Types: char
| string
| function_handle
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"
. Otherwise, the
software treats all columns of Tbl
, including W
,
as predictors when training the model.
By default, Weights
is ones(n,1)
, where n
is the number of observations in X
or Tbl
.
fitrnet
normalizes the weights to sum to 1.
Data Types: single
| double
| char
| string
CrossVal
— Flag to train cross-validated model
"off"
(default) | "on"
Flag to train a cross-validated model, specified as "on"
or
"off"
.
If you specify "on"
, then the software trains a cross-validated
model with 10 folds.
You can override this cross-validation setting using the
CVPartition
, Holdout
,
KFold
, or Leaveout
name-value argument.
You can use only one cross-validation name-value argument at a time to create a
cross-validated model.
Alternatively, cross-validate later by passing Mdl
to
crossval
.
Example: Crossval="on"
Data Types: char
| string
CVPartition
— Cross-validation partition
[]
(default) | cvpartition
object
Cross-validation partition, specified as a cvpartition
object that specifies the type of cross-validation and the
indexing for the training and validation sets.
To create a cross-validated model, you can specify only one of these four name-value
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: Suppose you create a random partition for 5-fold cross-validation on 500
observations by using cvp = cvpartition(500,KFold=5)
. Then, you can
specify the cross-validation partition by setting
CVPartition=cvp
.
Holdout
— Fraction of data for holdout validation
scalar value in the range (0,1)
Fraction of the data used for holdout validation, specified as a scalar value in the range
(0,1). If you specify Holdout=p
, then the software completes these
steps:
Randomly select and reserve
p*100
% of the data as validation data, and train the model using the rest of the data.Store the compact trained model in the
Trained
property of the cross-validated model.
To create a cross-validated model, you can specify only one of these four name-value
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: Holdout=0.1
Data Types: double
| single
KFold
— Number of folds
10
(default) | positive integer value greater than 1
Number of folds to use in the cross-validated model, specified as a positive integer value
greater than 1. If you specify KFold=k
, then the software completes
these steps:
Randomly partition the data into
k
sets.For each set, reserve the set as validation data, and train the model using the other
k
– 1 sets.Store the
k
compact trained models in ak
-by-1 cell vector in theTrained
property of the cross-validated model.
To create a cross-validated model, you can specify only one of these four name-value
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: KFold=5
Data Types: single
| double
Leaveout
— Leave-one-out cross-validation flag
"off"
(default) | "on"
Leave-one-out cross-validation flag, specified as "on"
or
"off"
. If you specify Leaveout="on"
, then for
each of the n observations (where n is the number
of observations, excluding missing observations, specified in the
NumObservations
property of the model), the software completes
these steps:
Reserve the one observation as validation data, and train the model using the other n – 1 observations.
Store the n compact trained models in an n-by-1 cell vector in the
Trained
property of the cross-validated model.
To create a cross-validated model, you can specify only one of these four name-value
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: Leaveout="on"
Data Types: char
| string
Note
You cannot use any cross-validation name-value argument together with the
OptimizeHyperparameters
name-value argument. You can modify the cross-validation forOptimizeHyperparameters
only by using theHyperparameterOptimizationOptions
name-value argument.Cross-validation options are not supported for multiresponse regression.
OptimizeHyperparameters
— Parameters to optimize
"none"
(default) | "auto"
| "all"
| string array or cell array of eligible parameter names | vector of optimizableVariable
objects
Parameters to optimize, specified as one of the following:
"none"
— Do not optimize."auto"
— Use["Activations","Lambda","LayerSizes","Standardize"]
."all"
— Optimize all eligible parameters.String array or cell array of eligible parameter names.
Vector of
optimizableVariable
objects, typically the output ofhyperparameters
.
The optimization attempts to minimize the cross-validation loss
(error) for fitrnet
by varying the parameters. To control the
cross-validation type and other aspects of the optimization, use the
HyperparameterOptimizationOptions
name-value argument. When you use
HyperparameterOptimizationOptions
, you can use the (compact) model size
instead of the cross-validation loss as the optimization objective by setting the
ConstraintType
and ConstraintBounds
options.
Note
The values of OptimizeHyperparameters
override any values you
specify using other name-value arguments. For example, setting
OptimizeHyperparameters
to "auto"
causes
fitrnet
to optimize hyperparameters corresponding to the
"auto"
option and to ignore any specified values for the
hyperparameters.
The eligible parameters for fitrnet
are:
Activations
—fitrnet
optimizesActivations
over the set{'relu','tanh','sigmoid','none'}
.Lambda
—fitrnet
optimizesLambda
over continuous values in the range[1e-5,1e5]/NumObservations
, where the value is chosen uniformly in the log transformed range.LayerBiasesInitializer
—fitrnet
optimizesLayerBiasesInitializer
over the two values{'zeros','ones'}
.LayerWeightsInitializer
—fitrnet
optimizesLayerWeightsInitializer
over the two values{'glorot','he'}
.LayerSizes
—fitrnet
optimizes over the three values1
,2
, and3
fully connected layers, excluding the final fully connected layer.fitrnet
optimizes each fully connected layer separately over1
through300
sizes in the layer, sampled on a logarithmic scale.Note
When you use the
LayerSizes
argument, the iterative display shows the size of each relevant layer. For example, if the current number of fully connected layers is3
, and the three layers are of sizes10
,79
, and44
respectively, the iterative display showsLayerSizes
for that iteration as[10 79 44]
.Note
To access up to five fully connected layers or a different range of sizes in a layer, use
hyperparameters
to select the optimizable parameters and ranges.Standardize
—fitrnet
optimizesStandardize
over the two values{true,false}
.
Set nondefault parameters by passing a vector of
optimizableVariable
objects that have nondefault values. As an
example, this code sets the range of NumLayers
to [1
5]
and optimizes Layer_4_Size
and
Layer_5_Size
:
load carsmall params = hyperparameters("fitrnet",[Horsepower,Weight],MPG); params(1).Range = [1 5]; params(10).Optimize = true; params(11).Optimize = true;
Pass params
as the value of
OptimizeHyperparameters
. For an example, see Custom Hyperparameter Optimization in Neural Network.
By default, the iterative display appears at the command line,
and plots appear according to the number of hyperparameters in the optimization. For the
optimization and plots, the objective function is log(1 + cross-validation loss). To control the iterative display, set the Verbose
field of
the 'HyperparameterOptimizationOptions'
name-value argument. To control the
plots, set the ShowPlots
field of the
'HyperparameterOptimizationOptions'
name-value argument.
For an example, see Minimize Cross-Validation Error in Neural Network.
Example: OptimizeHyperparameters="auto"
HyperparameterOptimizationOptions
— Options for optimization
HyperparameterOptimizationOptions
object | structure
Options for optimization, specified as a HyperparameterOptimizationOptions
object or a structure. This argument
modifies the effect of the OptimizeHyperparameters
name-value
argument. If you specify HyperparameterOptimizationOptions
, you must
also specify OptimizeHyperparameters
. All the options are optional.
However, you must set ConstraintBounds
and
ConstraintType
to return
AggregateOptimizationResults
. The options that you can set in a
structure are the same as those in the
HyperparameterOptimizationOptions
object.
Option | Values | Default |
---|---|---|
Optimizer |
| "bayesopt" |
ConstraintBounds | Constraint bounds for N optimization problems,
specified as an N-by-2 numeric matrix or
| [] |
ConstraintTarget | Constraint target for the optimization problems, specified as
| If you specify ConstraintBounds and
ConstraintType , then the default value is
"matlab" . Otherwise, the default value is
[] . |
ConstraintType | Constraint type for the optimization problems, specified as
| [] |
AcquisitionFunctionName | Type of acquisition function:
Acquisition functions whose names include
| "expected-improvement-per-second-plus" |
MaxObjectiveEvaluations | Maximum number of objective function evaluations. If you specify multiple
optimization problems using ConstraintBounds , the value of
MaxObjectiveEvaluations applies to each optimization
problem individually. | 30 for "bayesopt" and
"randomsearch" , and the entire grid for
"gridsearch" |
MaxTime | Time limit for the optimization, specified as a nonnegative real
scalar. The time limit is in seconds, as measured by | Inf |
NumGridDivisions | For Optimizer="gridsearch" , the number of values in each
dimension. The value can be a vector of positive integers giving the number of
values for each dimension, or a scalar that applies to all dimensions. This
option is ignored for categorical variables. | 10 |
ShowPlots | Logical value indicating whether to show plots of the optimization progress.
If this option is true , the software plots the best observed
objective function value against the iteration number. If you use Bayesian
optimization (Optimizer ="bayesopt" ), then
the software also plots the best estimated objective function value. The best
observed objective function values and best estimated objective function values
correspond to the values in the BestSoFar (observed) and
BestSoFar (estim.) columns of the iterative display,
respectively. You can find these values in the properties ObjectiveMinimumTrace and EstimatedObjectiveMinimumTrace of
Mdl.HyperparameterOptimizationResults . If the problem
includes one or two optimization parameters for Bayesian optimization, then
ShowPlots also plots a model of the objective function
against the parameters. | true |
SaveIntermediateResults | Logical value indicating whether to save the optimization results. If this
option is true , the software overwrites a workspace variable
named "BayesoptResults" at each iteration. The variable is a
BayesianOptimization object. If you
specify multiple optimization problems using
ConstraintBounds , the workspace variable is an AggregateBayesianOptimization object named
"AggregateBayesoptResults" . | false |
Verbose | Display level at the command line:
For details, see the | 1 |
UseParallel | Logical value indicating whether to run the Bayesian optimization in parallel, which requires Parallel Computing Toolbox™. Due to the nonreproducibility of parallel timing, parallel Bayesian optimization does not necessarily yield reproducible results. For details, see Parallel Bayesian Optimization. | false |
Repartition | Logical value indicating whether to repartition the cross-validation at
every iteration. If this option is A value of
| false |
Specify only one of the following three options. | ||
CVPartition | cvpartition object created by cvpartition | Kfold=5 if you do not specify a
cross-validation option |
Holdout | Scalar in the range (0,1) representing the holdout
fraction | |
Kfold | Integer greater than 1 |
Example: HyperparameterOptimizationOptions=struct(UseParallel=true)
Note
Hyperparameter optimization options are not supported for multiresponse regression.
Output Arguments
Mdl
— Trained neural network regression model
RegressionNeuralNetwork
model object | RegressionPartitionedNeuralNetwork
model object
Trained neural network regression model, returned as a RegressionNeuralNetwork
or RegressionPartitionedNeuralNetwork
model object.
If you set any of the name-value arguments CrossVal
,
CVPartition
, Holdout
,
KFold
, or Leaveout
, then
Mdl
is a RegressionPartitionedNeuralNetwork
model object. Otherwise, Mdl
is a
RegressionNeuralNetwork
model object.
To reference properties of Mdl
, use dot notation.
If you specify OptimizeHyperparameters
and
set the ConstraintType
and ConstraintBounds
options of
HyperparameterOptimizationOptions
, then Mdl
is an
N-by-1 cell array of model objects, where N is equal
to the number of rows in ConstraintBounds
. If none of the optimization
problems yields a feasible model, then each cell array value is []
.
AggregateOptimizationResults
— Aggregate optimization results
AggregateBayesianOptimization
object
Aggregate optimization results for multiple optimization problems, returned as an AggregateBayesianOptimization
object. To return
AggregateOptimizationResults
, you must specify
OptimizeHyperparameters
and
HyperparameterOptimizationOptions
. You must also specify the
ConstraintType
and ConstraintBounds
options of HyperparameterOptimizationOptions
. For an example that
shows how to produce this output, see Hyperparameter Optimization with Multiple Constraint Bounds.
More About
Neural Network Structure
The default neural network regression model has the following layer structure.
Structure | Description |
---|---|
| Input — This layer corresponds to the predictor data in
Tbl or X . |
First fully connected layer — This layer has 10 outputs by default.
| |
ReLU activation function —
| |
Final fully connected layer — This layer has one output for each response variable.
| |
Output — This layer corresponds to the predicted response values. |
For an example that shows how a regression neural network model with this layer structure returns predictions, see Predict Using Layer Structure of Regression Neural Network Model.
Tips
Always try to standardize the numeric predictors (see
Standardize
). Standardization makes predictors insensitive to the scales on which they are measured.After training a model, you can generate C/C++ code that predicts responses for new data. Generating C/C++ code requires MATLAB Coder™. For details, see Introduction to Code Generation.
Algorithms
Training Solver
fitrnet
uses a limited-memory Broyden-Fletcher-Goldfarb-Shanno
quasi-Newton algorithm (LBFGS) [3] as its loss function
minimization technique, where the software minimizes the mean squared error (MSE). The LBFGS
solver uses a standard line-search method with an approximation to the Hessian.
References
[1] Glorot, Xavier, and Yoshua Bengio. “Understanding the difficulty of training deep feedforward neural networks.” In Proceedings of the thirteenth international conference on artificial intelligence and statistics, pp. 249–256. 2010.
[2] He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. “Delving deep into rectifiers: Surpassing human-level performance on imagenet classification.” In Proceedings of the IEEE international conference on computer vision, pp. 1026–1034. 2015.
[3] Nocedal, J. and S. J. Wright. Numerical Optimization, 2nd ed., New York: Springer, 2006.
Extended Capabilities
Automatic Parallel Support
Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.
To perform parallel hyperparameter optimization, use the UseParallel=true
option in the HyperparameterOptimizationOptions
name-value argument in
the call to the fitrnet
function.
For more information on parallel hyperparameter optimization, see Parallel Bayesian Optimization.
For general information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™. (since R2024b)
fitrnet
fits the model on a GPU if at least one of the following applies:The input argument
X
is agpuArray
object.The input argument
Y
is agpuArray
object.The input argument
Tbl
containsgpuArray
predictor or response variables.
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2021aR2024b: Create neural network regression model 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 loss
object function to compute the regression loss, and the
predict
object function to predict the responses for new data.
In the call to fitrnet
, you can specify to standardize the response
variables by using the StandardizeResponses
name-value argument. You cannot use observations in rows,
validation data options, cross-validation options, or hyperparameter optimization options
when fitting a neural network model with multiple response variables.
R2024b: Specify gpuArray
inputs (requires Parallel Computing Toolbox)
fitrnet
now supports GPU arrays.
R2023b: A cross-validated regression neural network model is a RegressionPartitionedNeuralNetwork
object
Starting in R2023b, a cross-validated regression neural network model is a RegressionPartitionedNeuralNetwork
object. In previous releases, a cross-validated regression neural network model was a RegressionPartitionedModel
object.
You can create a RegressionPartitionedNeuralNetwork
object in two ways:
Create a cross-validated model from a regression neural network model object
RegressionNeuralNetwork
by using thecrossval
object function.Create a cross-validated model by using the
fitrnet
function and specifying one of the name-value argumentsCrossVal
,CVPartition
,Holdout
,KFold
, orLeaveout
.
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