kfoldPredict
Predict responses for observations in cross-validated regression model
Syntax
Description
specifies options using one or more name-value arguments. For example,
yFit
= kfoldPredict(CVMdl
,Name,Value
)'IncludeInteractions',true
specifies to include interaction terms in
computations for generalized additive models.
[
also returns the standard deviations and prediction intervals of the response variable,
evaluated at each observation in the predictor data yFit
,ySD
,yInt
] = kfoldPredict(___)CVMdl.X
, using
any of the input argument combinations in the previous syntaxes. This syntax applies only
to generalized additive models (GAM) for which the IsStandardDeviationFit
property of CVMdl
is
true
.
Examples
Compute Cross-Validation Loss Manually
When you create a cross-validated regression model, you can compute the mean squared error (MSE) by using the kfoldLoss
object function. Alternatively, you can predict responses for validation-fold observations using kfoldPredict
and compute the MSE manually.
Load the carsmall
data set. Specify the predictor data X
and the response data Y
.
load carsmall
X = [Cylinders Displacement Horsepower Weight];
Y = MPG;
Train a cross-validated regression tree model. By default, the software implements 10-fold cross-validation.
rng('default') % For reproducibility CVMdl = fitrtree(X,Y,'CrossVal','on');
Compute the 10-fold cross-validation MSE by using kfoldLoss
.
L = kfoldLoss(CVMdl)
L = 29.4963
Predict the responses yfit
by using the cross-validated regression model. Compute the mean squared error between yfit
and the true responses CVMdl.Y
. The computed MSE matches the loss value returned by kfoldLoss
.
yfit = kfoldPredict(CVMdl); mse = mean((yfit - CVMdl.Y).^2)
mse = 29.4963
Input Arguments
CVMdl
— Cross-validated partitioned regression model
RegressionPartitionedModel
object | RegressionPartitionedEnsemble
object | RegressionPartitionedGAM
object | RegressionPartitionedGP
object | RegressionPartitionedNeuralNetwork
object | RegressionPartitionedSVM
object
Cross-validated partitioned regression model, specified as a RegressionPartitionedModel
, RegressionPartitionedEnsemble
, RegressionPartitionedGAM
, RegressionPartitionedGP
, RegressionPartitionedNeuralNetwork
, or RegressionPartitionedSVM
object. You can create the object in two ways:
Pass a trained regression model listed in the following table to its
crossval
object function.Train a regression model using a function listed in the following table and specify one of the cross-validation name-value arguments for the function.
Regression Model | Function |
---|---|
RegressionEnsemble | fitrensemble |
RegressionGAM | fitrgam |
RegressionGP | fitrgp |
RegressionNeuralNetwork | fitrnet |
RegressionSVM | fitrsvm |
RegressionTree | fitrtree |
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: 'Alpha',0.01,'IncludeInteractions',false
specifies the
confidence level as 99% and excludes interaction terms from computations for a generalized
additive model.
Alpha
— Significance level
0.05 (default) | numeric scalar in [0,1]
Significance level for the confidence level of the prediction intervals
yInt
, specified as a numeric scalar in the range
[0,1]
. The confidence level of yInt
is equal
to 100(1 – Alpha)%
.
This argument is valid only for a generalized additive model object that includes
the standard deviation fit. That is, you can specify this argument only when
CVMdl
is RegressionPartitionedGAM
and the IsStandardDeviationFit
property of CVMdl
is
true
.
Example: 'Alpha',0.01
Data Types: single
| double
IncludeInteractions
— Flag to include interaction terms
true
| false
Flag to include interaction terms of the model, specified as true
or
false
. This argument is valid only for a generalized
additive model (GAM). That is, you can specify this argument only when
CVMdl
is RegressionPartitionedGAM
.
The default value is true
if the models in
CVMdl
(CVMdl.Trained
) contain
interaction terms. The value must be false
if the models do not
contain interaction terms.
Data Types: logical
PredictionForMissingValue
— Predicted response value to use for observations with missing predictor values
"median"
| "mean"
| numeric scalar
Since R2023b
Predicted response value to use for observations with missing predictor values,
specified as "median"
, "mean"
, or a numeric
scalar. This argument is valid only for a Gaussian process regression, neural network,
or support vector machine model. That is, you can specify this argument only when
CVMdl
is a RegressionPartitionedGP
,
RegressionPartitionedNeuralNetwork
, or
RegressionPartitionedSVM
object.
Value | Description |
---|---|
"median" |
This value is
the default when |
"mean" | kfoldPredict uses the mean of the observed response
values in the training-fold data as the predicted response value for
observations with missing predictor values. |
Numeric scalar | kfoldPredict uses this value as the predicted
response value for observations with missing predictor values. |
Example: "PredictionForMissingValue","mean"
Example: "PredictionForMissingValue",NaN
Data Types: single
| double
| char
| string
Output Arguments
yFit
— Predicted responses
numeric vector
Predicted responses, returned as an n-by-1 numeric vector, where
n is the number of observations. (n is
size(CVMdl.X,1)
when observations are in rows.) Each entry of
yFit
corresponds to the predicted response for the corresponding
row of CVMdl.X
.
If you use a holdout validation technique to create CVMdl
(that
is, if CVMdl.KFold
is 1
), then
yFit
has NaN
values for training-fold
observations.
ySD
— Standard deviations of response variable
column vector
Standard deviations of the response variable, evaluated at each observation in the
predictor data
, returned as a column
vector of length n, where n is the number of
observations in CVMdl
.X
. The
CVMdl
.Xi
th element ySD(i)
contains the standard
deviation of the i
th response for the i
th
observation CVMdl.X(i,:)
, estimated using the trained standard
deviation model in CVMdl
.
This argument is valid only for a generalized additive model object that includes
the standard deviation fit. That is, kfoldPredict
can return this
argument only when CVMdl
is RegressionPartitionedGAM
and the IsStandardDeviationFit
property of CVMdl
is
true
.
yInt
— Prediction intervals of response variable
two-column matrix
Prediction intervals of the response variable, evaluated at each observation in the
predictor data
, returned as an
n-by-2 matrix, where n is the number of
observations in CVMdl
.X
. The
CVMdl
.Xi
th row yInt(i,:)
contains the estimated
100(1 –
prediction
interval of the Alpha
)%i
th response for the i
th
observation CVMdl.X(i,:)
using
. The ySD
(i)Alpha
value
is the probability that the prediction interval does not contain the true response value
CVMdl.Y(i)
. The first column of yInt
contains
the lower limits of the prediction intervals, and the second column contains the upper
limits.
This argument is valid only for a generalized additive model object that includes
the standard deviation fit. That is, kfoldPredict
can return this
argument only when CVMdl
is RegressionPartitionedGAM
and the IsStandardDeviationFit
property of CVMdl
is
true
.
Extended Capabilities
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
This function fully supports GPU arrays for the following models.
RegressionPartitionedModel
object fitted usingfitrtree
, or by passing aRegressionTree
object tocrossval
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2011aR2024b: Specify GPU arrays for neural network models (requires Parallel Computing Toolbox)
kfoldPredict
fully supports GPU arrays for RegressionPartitionedNeuralNetwork
models.
R2023b: Specify predicted response value to use for observations with missing predictor values
Starting in R2023b, when you predict or compute the loss, some regression models allow you to specify the predicted response value for observations with missing predictor values. Specify the PredictionForMissingValue
name-value argument to use a numeric scalar, the training set median, or the training set mean as the predicted value. When computing the loss, you can also specify to omit observations with missing predictor values.
This table lists the object functions that support the
PredictionForMissingValue
name-value argument. By default, the
functions use the training set median as the predicted response value for observations with
missing predictor values.
Model Type | Model Objects | Object Functions |
---|---|---|
Gaussian process regression (GPR) model | RegressionGP , CompactRegressionGP | loss , predict , resubLoss , resubPredict |
RegressionPartitionedGP | kfoldLoss , kfoldPredict | |
Gaussian kernel regression model | RegressionKernel | loss , predict |
RegressionPartitionedKernel | kfoldLoss , kfoldPredict | |
Linear regression model | RegressionLinear | loss , predict |
RegressionPartitionedLinear | kfoldLoss , kfoldPredict | |
Neural network regression model | RegressionNeuralNetwork , CompactRegressionNeuralNetwork | loss , predict , resubLoss , resubPredict |
RegressionPartitionedNeuralNetwork | kfoldLoss , kfoldPredict | |
Support vector machine (SVM) regression model | RegressionSVM , CompactRegressionSVM | loss , predict , resubLoss , resubPredict |
RegressionPartitionedSVM | kfoldLoss , kfoldPredict |
In previous releases, the regression model loss
and predict
functions listed above used NaN
predicted response values for observations with missing predictor values. The software omitted observations with missing predictor values from the resubstitution ("resub") and cross-validation ("kfold") computations for prediction and loss.
R2023a: GPU support for RegressionPartitionedSVM
models
Starting in R2023a, kfoldPredict
fully supports GPU arrays for RegressionPartitionedSVM
models.
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