RegressionPartitionedQuantileModel

Cross-validated quantile model for regression

Since R2025a

Description

RegressionPartitionedQuantileModel is a set of quantile regression models trained on cross-validated folds. You can estimate the quality of the object by using one or more kfold functions: kfoldPredict, kfoldLoss, and kfoldfun.

Each kfold function uses models trained on training-fold (in-fold) observations to predict the response for validation-fold (out-of-fold) observations. For example, when you use kfoldPredict with a k-fold cross-validated model, the software estimates a response for every observation using the model trained without that observation. For more information, see Partitioned Models.

Creation

You can create a RegressionPartitionedQuantileModel object in two ways:

Create a cross-validated model from a quantile regression model object by using the crossval object function.
Create a cross-validated model by using the fitrqlinear function and specifying one of the name-value arguments CrossVal, CVPartition, Holdout, KFold, or Leaveout.

Properties

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Cross-Validation Properties

`CrossValidatedModel` — Cross-validated model name
Read-only: `'QuantileLinear'`

This property is read-only.

Cross-validated model name, returned as 'QuantileLinear'.

Data Types: char

`KFold` — Number of cross-validated folds
Read-only: positive integer

This property is read-only.

Number of cross-validated folds, returned as a positive integer.

Data Types: double

`ModelParameters` — Cross-validation parameter values
Read-only: `EnsembleParams` object

This property is read-only.

Cross-validation parameter values, returned as an EnsembleParams object. The parameter values correspond to the values of the name-value arguments used to cross-validate the quantile regression model. ModelParameters does not contain estimated parameters.

You can access the properties of ModelParameters using dot notation.

`Partition` — Data partition
Read-only: `cvpartition` object

This property is read-only.

Data partition indicating how the software splits the data into cross-validation folds, returned as a cvpartition object.

`Trained` — Compact models trained on cross-validation folds
Read-only: cell array of `CompactRegressionQuantileLinear` model objects

This property is read-only.

Compact models trained on the cross-validation folds, returned as a cell array of CompactRegressionQuantileLinear model objects. Trained has k cells, where k is the number of folds.

Data Types: cell

Other Regression Quantile Properties

`Quantiles` — Quantiles
Read-only: vector of values in the range [0,1]

This property is read-only.

Quantiles used to train the quantile regression model, returned as a vector of values in the range [0,1].

Data Types: double

`PredictorNames` — Predictor variable names
Read-only: cell array of character vectors

This property is read-only.

Predictor variable names, returned as a cell array of character vectors. The order of the elements in PredictorNames corresponds to the order in which the predictor names appear in the training data.

Data Types: cell

`CategoricalPredictors` — Categorical predictor indices
Read-only: vector of positive integers | `[]`

This property is read-only.

Categorical predictor indices, returned as a vector of positive integers. Assuming that the predictor data contains observations in rows, CategoricalPredictors contains index values corresponding to the columns of the predictor data that contain categorical predictors. If none of the predictors are categorical, then this property is empty ([]).

Data Types: double

`NumObservations` — Number of observations
Read-only: positive integer scalar

This property is read-only.

Number of observations in the training data stored in X and Y, returned as a positive integer scalar.

Data Types: double

`ResponseName` — Response variable name
Read-only: character vector

This property is read-only.

Response variable name, returned as a character vector.

Data Types: char

`ResponseTransform` — Response transformation function
`"none"` | function handle

Response transformation function, specified as "none" or a function handle. ResponseTransform describes how the software transforms raw response values.

For a MATLAB^® function or a function that you define, enter its function handle. For example, you can enter Mdl.ResponseTransform = @function, where function accepts a numeric vector of the original responses and returns a numeric vector of the same size containing the transformed responses.

Data Types: char | string | function_handle

`W` — Observation weights
Read-only: numeric vector

This property is read-only.

Observation weights, returned as an n-by-1 numeric vector, where n is the number of observations (NumObservations).

The software normalizes the observation weights so that the elements of W sum to 1.

Data Types: single | double

`X` — Unstandardized predictors
Read-only: numeric matrix | table

This property is read-only.

Unstandardized predictors used to cross-validate the model, returned as a numeric matrix or a table. X retains its original orientation, with observations in rows or columns depending on the value of the ObservationsIn name-value argument in the call to the fitting function.

Data Types: single | double | table

`Y` — Response values
Read-only: numeric vector

This property is read-only.

Response values used to cross-validate the model, returned as a numeric vector. Each row of Y represents the response value of the corresponding observation in X.

Data Types: single | double

Object Functions

`kfoldLoss`	Loss for cross-validated partitioned quantile regression model
`kfoldPredict`	Predict responses for observations in cross-validated quantile regression model
`kfoldfun`	Cross-validate function for quantile regression

Examples

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Cross-Validate Quantile Linear Regression Model

Open Live Script

Cross-validate a quantile linear regression model using the default 10-fold cross-validation.

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);

Train a quantile linear 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, change the beta tolerance to 1e-6 instead of the default value 1e-4, and use a ridge (L2) regularization term of 1.

Mdl = fitrqlinear(X,Y,Quantiles=[0.25,0.50,0.75], ...
    BetaTolerance=1e-6,Lambda=1)

Mdl = 
  RegressionQuantileLinear
             ResponseName: 'Y'
    CategoricalPredictors: []
        ResponseTransform: 'none'
                     Beta: [4×3 double]
                     Bias: [17.0306 22.5291 29.0044]
                Quantiles: [0.2500 0.5000 0.7500]


  Properties, Methods

Mdl is a trained RegressionQuantileLinear model object.

Cross-validate the regression model using 10-fold cross-validation. During cross-validation, the software completes these steps:

Randomly partition the data into 10 sets (folds) of equal size.
For each set, reserve the set as validation data, and train a quantile linear regression model on the other nine sets.
Store the 10 trained models in a 10-by-1 cell vector in the Trained property of the cross-validated model object.

CVMdl = crossval(Mdl)

CVMdl = 
  RegressionPartitionedQuantileModel
    CrossValidatedModel: 'QuantileLinear'
         PredictorNames: {'x1'  'x2'  'x3'  'x4'}
           ResponseName: 'Y'
        NumObservations: 392
                  KFold: 10
              Partition: [1×1 cvpartition]
      ResponseTransform: 'none'
              Quantiles: [0.2500 0.5000 0.7500]


  Properties, Methods

CVMdl is a RegressionPartitionedQuantileModel object.

Display the first model in CVMdl.Trained.

FirstModel = CVMdl.Trained{1}

FirstModel = 
  CompactRegressionQuantileLinear
           PredictorNames: {'x1'  'x2'  'x3'  'x4'}
             ResponseName: 'Y'
    CategoricalPredictors: []
        ResponseTransform: 'none'
                     Beta: [4×3 double]
                     Bias: [17.0004 22.5029 29.0247]
                Quantiles: [0.2500 0.5000 0.7500]


  Properties, Methods

FirstModel is the first of the 10 trained models contained in CVMdl. The trained models are all CompactRegressionQuantileLinear objects.

After creating a cross-validated quantile regression model object, you can estimate the generalized quantile loss by passing the model to kfoldLoss.

Algorithms

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Partitioned Models

You can create partitioned models by using k-fold cross-validation, holdout validation, leave-one-out cross-validation, or resubstitution.

k-fold cross-validation — The software divides the observations into KFold disjoint folds, each of which has approximately the same number of observations. The software trains KFold models (Trained), and each model is trained on KFold – 1 of the folds. When you use kfoldPredict, each model predicts the response values for the remaining fold.
Holdout validation — The software partitions the observations into a training set and a validation set. The software trains one model (Trained) using the training set. When you use kfoldPredict, the model predicts the response values for the validation set.
Leave-one-out cross-validation — The software creates NumObservations folds, where each observation is a fold. The software trains NumObservations models (Trained), and each model is trained on NumObservations – 1 of the folds. When you use kfoldPredict, each model predicts the response for the remaining fold (observation).
Resubstitution — The software does not partition the data. The software trains one model (Trained) on the entire data set. When you use kfoldPredict, the model predicts the response values for all observations.

Version History

Introduced in R2025a

RegressionPartitionedQuantileModel

Description

Creation

Properties

Cross-Validation Properties

CrossValidatedModel — Cross-validated model name Read-only: 'QuantileLinear'

KFold — Number of cross-validated folds Read-only: positive integer

ModelParameters — Cross-validation parameter values Read-only: EnsembleParams object

Partition — Data partition Read-only: cvpartition object

Trained — Compact models trained on cross-validation folds Read-only: cell array of CompactRegressionQuantileLinear model objects

Other Regression Quantile Properties

Quantiles — Quantiles Read-only: vector of values in the range [0,1]

PredictorNames — Predictor variable names Read-only: cell array of character vectors

CategoricalPredictors — Categorical predictor indices Read-only: vector of positive integers | []

NumObservations — Number of observations Read-only: positive integer scalar

ResponseName — Response variable name Read-only: character vector

ResponseTransform — Response transformation function "none" | function handle

W — Observation weights Read-only: numeric vector

X — Unstandardized predictors Read-only: numeric matrix | table

Y — Response values Read-only: numeric vector

Object Functions

Examples

Cross-Validate Quantile Linear Regression Model

Algorithms

Partitioned Models

Version History

See Also

`CrossValidatedModel` — Cross-validated model name
Read-only: `'QuantileLinear'`

`KFold` — Number of cross-validated folds
Read-only: positive integer

`ModelParameters` — Cross-validation parameter values
Read-only: `EnsembleParams` object

`Partition` — Data partition
Read-only: `cvpartition` object

`Trained` — Compact models trained on cross-validation folds
Read-only: cell array of `CompactRegressionQuantileLinear` model objects

`Quantiles` — Quantiles
Read-only: vector of values in the range [0,1]

`PredictorNames` — Predictor variable names
Read-only: cell array of character vectors

`CategoricalPredictors` — Categorical predictor indices
Read-only: vector of positive integers | `[]`

`NumObservations` — Number of observations
Read-only: positive integer scalar

`ResponseName` — Response variable name
Read-only: character vector

`ResponseTransform` — Response transformation function
`"none"` | function handle

`W` — Observation weights
Read-only: numeric vector

`X` — Unstandardized predictors
Read-only: numeric matrix | table

`Y` — Response values
Read-only: numeric vector