# 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, $$f\left(x\right)=x\beta +b.$$

*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: $$\ell \left[y,f\left(x\right)\right]=\mathrm{max}\left[0,\left|y-f\left(x\right)\right|-\epsilon \right]$$ `'mse'`

MSE: $$\ell \left[y,f\left(x\right)\right]={\left[y-f\left(x\right)\right]}^{2}$$ `'epsiloninsensitive'`

is appropriate for SVM learners only.Specify your own function using function handle notation.

Assume that

`n`

is the number of observations in`X`

. Your function must have this signaturewhere:`lossvalue =`

(Y,Yhat,W)`lossfun`

The output argument

`lossvalue`

is a scalar.You specify the function name (

).`lossfun`

`Y`

is an`n`

-dimensional vector of observed responses.`kfoldLoss`

passes the input argument`Y`

in for`Y`

.`Yhat`

is an`n`

-dimensional vector of predicted responses, which is similar to the output of`predict`

.`W`

is an`n`

-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'`

, then`L`

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 fold)`j`

.`j`

To estimate `L`

, `kfoldLoss`

uses the
data that created `CVMdl`

.

## Version History

**Introduced in R2018b**

### 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.

## See Also

`fitrkernel`

| `RegressionKernel`

| `RegressionPartitionedKernel`

| `kfoldPredict`

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