kfoldLoss
Regression loss for cross-validated kernel regression model
Description
returns the mean squared error (MSE) with additional options specified by one or more
name-value arguments. For example, you can specify the regression-loss function or which
folds to use for loss calculation.L
= kfoldLoss(CVMdl
,Name,Value
)
Examples
Compute Loss for Cross-Validated Kernel Regression Models
Simulate sample data:
rng(0,'twister'); % For reproducibility n = 1000; x = linspace(-10,10,n)'; y = 1 + x*2e-2 + sin(x)./x + 0.2*randn(n,1);
Cross-validate a kernel regression model.
CVMdl = fitrkernel(x,y,'Kfold',5);
fitrkernel
implements 5-fold cross-validation. CVMdl
is a RegressionPartitionedKernel
model. It contains the property Trained
, which is a 5-by-1 cell array holding 5 RegressionKernel
models that the software trained using the training set.
Compute the epsilon-insensitive loss for each fold for observations that fitrkernel
did not use in training the folds.
L = kfoldLoss(CVMdl,'LossFun','epsiloninsensitive','Mode','individual')
L = 5×1
0.1261
0.1247
0.1107
0.1237
0.1131
Input Arguments
CVMdl
— Cross-validated kernel regression model
RegressionPartitionedKernel
model object
Cross-validated kernel regression model, specified as a RegressionPartitionedKernel
model object. You can create a
RegressionPartitionedKernel
model using fitrkernel
and specifying any of the cross-validation name-value pair arguments, for example,
CrossVal
.
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: 'LossFun','epsiloninsensitive','Mode','individual'
specifies
kfoldLoss
to return the epsilon-insensitive loss for each
fold.
Folds
— Fold indices to use for response prediction
1:CVMdl.KFold
(default) | numeric vector of positive integers
Fold indices to use for response prediction, specified as a numeric vector of positive
integers. The elements of Folds
must range from 1
through CVMdl.KFold
.
Example: Folds=[1 4 10]
Data Types: single
| double
LossFun
— Loss function
'mse'
(default) | 'epsiloninsensitive'
| function handle
Loss function, specified as the comma-separated pair consisting of
'LossFun'
and a built-in loss function name or function handle.
The following table lists the available loss functions. Specify one using its corresponding character vector or string scalar. Also, in the table,
β is a vector of p coefficients.
x is an observation from p predictor variables.
b is the scalar bias.
Value Description 'epsiloninsensitive'
Epsilon-insensitive loss: 'mse'
MSE: 'epsiloninsensitive'
is appropriate for SVM learners only.Specify your own function using function handle notation.
Assume that
n
is the number of observations inX
. Your function must have this signaturewhere:lossvalue =
lossfun
(Y,Yhat,W)The output argument
lossvalue
is a scalar.You specify the function name (
lossfun
).Y
is ann
-dimensional vector of observed responses.kfoldLoss
passes the input argumentY
in forY
.Yhat
is ann
-dimensional vector of predicted responses, which is similar to the output ofpredict
.W
is ann
-by-1 numeric vector of observation weights.
Data Types: char
| string
| function_handle
Mode
— Loss aggregation level
"average"
(default) | "individual"
Loss aggregation level, specified as "average"
or
"individual"
.
Value | Description |
---|---|
"average" | Returns losses averaged over all folds |
"individual" | Returns losses for each fold |
Example: Mode="individual"
PredictionForMissingValue
— Predicted response value to use for observations with missing predictor values
"median"
(default) | "mean"
| "omitted"
| numeric scalar
Since R2023b
Predicted response value to use for observations with missing predictor values,
specified as "median"
, "mean"
,
"omitted"
, or a numeric scalar.
Value | Description |
---|---|
"median" | kfoldLoss uses the median of the observed response
values in the training-fold data as the predicted response value for
observations with missing predictor values. |
"mean" | kfoldLoss uses the mean of the observed response
values in the training-fold data as the predicted response value for
observations with missing predictor values. |
"omitted" | kfoldLoss excludes observations with missing
predictor values from the loss computation. |
Numeric scalar | kfoldLoss uses this value as the predicted
response value for observations with missing predictor values. |
If an observation is missing an observed response value or an observation weight,
then kfoldLoss
does not use the observation in the loss
computation.
Example: "PredictionForMissingValue","omitted"
Data Types: single
| double
| char
| string
Output Arguments
L
— Cross-validated regression losses
numeric scalar | numeric vector
Cross-validated regression losses, returned as a numeric scalar or vector. The
interpretation of L
depends on LossFun
.
If
Mode
is'average'
, thenL
is a scalar.Otherwise,
L
is a k-by-1 vector, where k is the number of folds.L(
is the average regression loss over foldj
)j
.
To estimate L
, kfoldLoss
uses the
data that created CVMdl
.
Version History
Introduced in R2018bR2023b: 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.
See Also
fitrkernel
| RegressionKernel
| RegressionPartitionedKernel
| kfoldPredict
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