fitrqnet
Syntax
Description
returns a trained regression quantile neural network model Mdl
= fitrqnet(Tbl
,ResponseVarName
)Mdl
. The
function trains the model using the predictors in the table Tbl
and the
response values in the ResponseVarName
table variable.
By default, the function uses the median (0.5 quantile).
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 the quantiles by
using the Mdl
= fitrqnet(___,Name=Value
)Quantiles
name-value argument.
Examples
Fit Quantile Neural Network Regression Model
Fit a quantile neural network regression model using the 0.25, 0.50, and 0.75 quantiles.
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
, Displacement
, Horsepower
, and Weight
. Store the response variable MPG
in the variable Y
.
load carbig
X = [Acceleration,Displacement,Horsepower,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(0,"twister") % For reproducibility of the partition c = cvpartition(length(Y),"Holdout",0.20); trainingIdx = training(c); XTrain = X(trainingIdx,:); YTrain = Y(trainingIdx); testIdx = test(c); XTest = X(testIdx,:); YTest = Y(testIdx);
Train a quantile neural network regression model. Specify to use the 0.25
, 0.50
, and 0.75
quantiles (that is, the lower quartile, median, and upper quartile). To improve the model fit, standardize the numeric predictors. Use a ridge (L2) regularization term of 1
. Adding a regularization term can help prevent quantile crossing.
Mdl = fitrqnet(XTrain,YTrain,Quantiles=[0.25,0.50,0.75], ...
Standardize=true,Lambda=0.05)
Mdl = RegressionQuantileNeuralNetwork ResponseName: 'Y' CategoricalPredictors: [] LayerSizes: 10 Activations: 'relu' OutputLayerActivation: 'none' Quantiles: [0.2500 0.5000 0.7500]
Mdl
is a RegressionQuantileNeuralNetwork
model object. You can use dot notation to access the properties of Mdl
. For example, Mdl.LayerWeights
and Mdl.LayerBiases
contain the weights and biases, respectively, for the fully connected layers of the trained model.
In this example, you can use the layer weights, layer biases, predictor means, and predictor standard deviations directly to predict the test set responses for each of the three quantiles in Mdl.Quantiles
. In general, you can use the predict
object function to make quantile predictions.
firstFCStep = (Mdl.LayerWeights{1})*((XTest-Mdl.Mu)./Mdl.Sigma)' ...
+ Mdl.LayerBiases{1};
reluStep = max(firstFCStep,0);
finalFCStep = (Mdl.LayerWeights{end})*reluStep + Mdl.LayerBiases{end};
predictedY = finalFCStep'
predictedY = 78×3
13.9602 15.1340 16.6884
11.2792 12.2332 13.4849
19.5525 21.7303 23.9473
22.6950 25.5260 28.1201
10.4533 11.3377 12.4984
17.6935 19.5194 21.5152
12.4312 13.4797 14.8614
11.7998 12.7963 14.1071
16.6860 18.3305 20.2070
24.1142 27.0301 29.7811
⋮
isequal(predictedY,predict(Mdl,XTest))
ans = logical
1
Each column of predictedY
corresponds to a separate quantile (0.25, 0.5, or 0.75).
Visualize the predictions of the quantile neural network regression model. First, create a grid of predictor values.
minX = floor(min(X))
minX = 1×4
8 68 46 1613
maxX = ceil(max(X))
maxX = 1×4
25 455 230 5140
gridX = zeros(100,size(X,2)); for p = 1:size(X,2) gridp = linspace(minX(p),maxX(p))'; gridX(:,p) = gridp; end
Next, use the trained model Mdl
to predict the response values for the grid of predictor values.
gridY = predict(Mdl,gridX)
gridY = 100×3
31.2419 35.0661 38.6357
30.8637 34.6317 38.1573
30.4854 34.1972 37.6789
30.1072 33.7627 37.2005
29.7290 33.3283 36.7221
29.3507 32.8938 36.2436
28.9725 32.4593 35.7652
28.5943 32.0249 35.2868
28.2160 31.5904 34.8084
27.8378 31.1560 34.3300
⋮
For each observation in gridX
, the predict
object function returns predictions for the quantiles in Mdl.Quantiles
.
View the gridY
predictions for the second predictor (Displacement
). Compare the quantile predictions to the true test data values.
predictorIdx = 2; plot(XTest(:,predictorIdx),YTest,".") hold on plot(gridX(:,predictorIdx),gridY(:,1)) plot(gridX(:,predictorIdx),gridY(:,2)) plot(gridX(:,predictorIdx),gridY(:,3)) hold off xlabel("Predictor (Displacement)") ylabel("Response (MPG)") legend(["True values","0.25 predicted values", ... "0.50 predicted values","0.75 predicted values"]) title("Test Data")
The red curve shows the predictions for the 0.25 quantile, the yellow curve shows the predictions for the 0.50 quantile, and the purple curve shows the predictions for the 0.75 quantile. The blue points indicate the true test data values.
Notice that the quantile prediction curves do not cross each other.
Prevent Quantile Crossing Using Regularization
When training a quantile neural network regression model, you can use a ridge (L2) regularization term to prevent quantile crossing.
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
, Cylinders
, Displacement
, and so on, as well as the response variable MPG
.
load carbig cars = table(Acceleration,Cylinders,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 using cvpartition
. Use approximately 80% of the observations as training data, and 20% of the observations as test data.
rng(0,"twister") % For reproducibility of the data partition c = cvpartition(height(cars),"Holdout",0.20); trainingIdx = training(c); carsTrain = cars(trainingIdx,:); testIdx = test(c); carsTest = cars(testIdx,:);
Train a quantile neural network regression model. Use the 0.25
, 0.50
, and 0.75
quantiles (that is, the lower quartile, median, and upper quartile). To improve the model fit, standardize the numeric predictors before training.
Mdl = fitrqnet(carsTrain,"MPG",Quantiles=[0.25 0.5 0.75], ... Standardize=true);
Mdl
is a RegressionNeuralNetwork
model object.
Determine if the test data predictions for the quantiles in Mdl.Quantiles
cross each other by using the predict
object function of Mdl
. The crossingIndicator
output argument contains a value of 1
(true
) for any observation with quantile predictions that cross.
[~,crossingIndicator] = predict(Mdl,carsTest); sum(crossingIndicator)
ans = 2
In this example, two of the observations in carsTest
have quantile predictions that cross each other.
To prevent quantile crossing, specify the Lambda
name-value argument in the call to fitrqnet
. Use a 0.05
ridge (L2) penalty term.
newMdl = fitrqnet(carsTrain,"MPG",Quantiles=[0.25 0.5 0.75], ... Standardize=true,Lambda=0.05); [predictedY,newCrossingIndicator] = predict(newMdl,carsTest); sum(newCrossingIndicator)
ans = 0
With regularization, the predictions for the test data set do not cross for any observations.
Visualize the predictions returned by newMdl
by using a scatter plot with a reference line. Plot the predicted values along the vertical axis and the true response values along the horizontal axis. Points on the reference line indicate correct predictions.
plot(carsTest.MPG,predictedY(:,1),".") hold on plot(carsTest.MPG,predictedY(:,2),".") plot(carsTest.MPG,predictedY(:,3),".") plot(carsTest.MPG,carsTest.MPG) hold off xlabel("True MPG") ylabel("Predicted MPG") legend(["0.25 quantile values","0.50 quantile values", ... "0.75 quantile values","Reference line"], ... Location="southeast") title("Test Data")
Blue points correspond to the 0.25 quantile, red points correspond to the 0.50 quantile, and yellow points correspond to the 0.75 quantile.
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.
Optionally, Tbl
can contain one additional column for the response
variable. Multicolumn variables and cell arrays other than cell arrays of character
vectors are not allowed.
If
Tbl
contains the response variable, and you want to use all remaining variables inTbl
as predictors, then specify the response variable by usingResponseVarName
.If
Tbl
contains the response variable, and you want to use only a subset of the remaining variables inTbl
as predictors, then specify a formula by usingformula
.If
Tbl
does not contain the response variable, then specify a response variable by usingY
. The length of the response variable and the number of rows inTbl
must be equal.
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.
You must specify ResponseVarName
as a character vector or string
scalar. For example, if Tbl
stores the response variable
Y
as Tbl.Y
, then specify it as
"Y"
. Otherwise, the software treats all columns of
Tbl
, including Y
, as predictors when
training the model.
Data Types: char
| string
formula
— Explanatory model of response variable and subset of predictor variables
character vector | string scalar
Explanatory model of the response variable and a subset of the predictor variables,
specified as a character vector or string scalar in the form
"Y~x1+x2+x3"
. In this form, Y
represents the
response variable, 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
.
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
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.
The length of Y
and the number of observations in
X
must be equal.
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
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, a row in
X
orValidationData{1}
)NaN
value or0
weight (for example, a value inWeights
orValidationData{3}
)
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.
Example: fitrqnet(Tbl,"MPG",Quantiles=[0.25 0.5
0.75],Standardize=true)
specifies to use the 0.25, 0.5, and 0.75 quantiles and
to standardize the data before training.
Quantiles
— Quantiles
0.5
(default) | vector of values in the range [0,1]
Quantiles to use for training Mdl
, specified as a vector of
values in the range [0,1]. The function trains a model that separates the bottom 100*q percent of training responses from the top 100*(1 – q) percent of training responses for each quantile
q.
Example: Quantiles=[0.25 0.5 0.75]
Data Types: single
| double
LayerSizes
— Sizes of fully connected layers
10
(default) | positive integer vector
Sizes of the fully connected layers in the quantile neural network regression
model, specified as a positive integer vector. Element i of
LayerSizes
is the number of outputs in the fully connected
layer i of the neural network model.
LayerSizes
does not include the size of the final fully
connected layer. For more information, see Quantile Neural Network Structure.
Example: LayerSizes=[100 25 10]
Data Types: single
| double
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 quantile neural network regression 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 Quantile Neural Network Structure).If you specify an array of activation functions, then element i of
Activations
is the activation function for layer i of the neural network model.
Example: Activations="sigmoid"
Data Types: char
| string
| cell
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.
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 constructs the objective function for minimization from the quantile loss averaged over the quantiles (see Quantile Loss) 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
Verbose
— Verbosity level
0
(default) | 1
Verbosity level, specified as 0
or 1
. The
Verbose
name-value argument controls the display of diagnostic
information at the command line.
Value | Description |
---|---|
0 | fitrqnet does not display diagnostic
information. |
1 | fitrqnet periodically displays diagnostic
information. |
fitrqnet
stores the diagnostic information in
Mdl
. Use Mdl.ConvergenceInfo.History
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
InitialStepSize
— Initial step size
[]
(default) | positive scalar | "auto"
Initial step size, specified as a positive scalar or "auto"
. By
default, fitrqnet
does not use the initial step size to
determine the initial Hessian approximation used in training the model. 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 fitrqnet
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.ConvergenceCriterion
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
consecutively. You can check the Mdl.ConvergenceInfo.History
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
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
), fitrqnet
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
), fitrqnet
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, fitrqnet
creates
dummy variables using two different schemes, depending on whether a categorical variable
is unordered or ordered. For an unordered categorical variable,
fitrqnet
creates one dummy variable for each level of the
categorical variable. For an ordered categorical variable,
fitrqnet
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,fitrqnet
uses only the predictor variables inPredictorNames
and the response variable during training.PredictorNames
must be a subset ofTbl.Properties.VariableNames
and cannot include the name of the 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 name
"Y"
(default) | character vector | string scalar
Response variable name, specified as a character vector or string scalar.
If you supply
Y
, then you can useResponseName
to specify a name for the response variable.If you supply
ResponseVarName
orformula
, then you cannot useResponseName
.
Example: ResponseName="response"
Data Types: char
| string
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 should accept a vector
(the original response values) and return a vector 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
.
fitrqnet
normalizes the weights to sum to 1.
Data Types: single
| double
| char
| string
Output Arguments
Mdl
— Trained quantile neural network model
RegressionQuantileNeuralNetwork
model object
Trained quantile neural network model, returned as a RegressionQuantileNeuralNetwork
model object.
To reference properties of Mdl
, use dot notation.
More About
Quantile Neural Network Structure
The default quantile 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 quantile
specified by the
| |
Output — This layer corresponds to the predicted response values. |
Tips
You can use the α/2 and 1 – α/2 quantiles to create a prediction interval that captures an estimated 100*(1 – α) percent of the variation in the response.
Algorithms
Training Solver
fitrqnet
uses a limited-memory Broyden-Fletcher-Goldfarb-Shanno
quasi-Newton algorithm (LBFGS) [3] as its loss function
minimization technique, where the software minimizes the quantile loss averaged over the
quantiles (see Quantile Loss). The LBFGS solver uses a
standard line-search method with an approximation to the Hessian.
Version History
Introduced in R2024b
See Also
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)