# RegressionEnsemble

Ensemble regression

## Description

`RegressionEnsemble`

combines a set of trained
weak learner models and data on which these learners were trained. It can predict
ensemble response for new data by aggregating predictions from its weak
learners.

## Creation

### Description

Create a regression ensemble object using `fitrensemble`

.

## Properties

`BinEdges`

— Bin edges for numeric predictors

cell array of *p* numeric vectors

This property is read-only.

Bin edges for numeric predictors, specified as a cell array of *p* numeric vectors, where *p* is the number of predictors. Each vector includes the bin edges for a numeric predictor. The element in the cell array for a categorical predictor is empty because the software does not bin categorical predictors.

The software bins numeric predictors only if you specify the `'NumBins'`

name-value argument as a positive integer scalar when training a model with tree learners.
The `BinEdges`

property is empty if the `'NumBins'`

value is empty (default).

You can reproduce the binned predictor data `Xbinned`

by using the
`BinEdges`

property of the trained model
`mdl`

.

```
X = mdl.X; % Predictor data
Xbinned = zeros(size(X));
edges = mdl.BinEdges;
% Find indices of binned predictors.
idxNumeric = find(~cellfun(@isempty,edges));
if iscolumn(idxNumeric)
idxNumeric = idxNumeric';
end
for j = idxNumeric
x = X(:,j);
% Convert x to array if x is a table.
if istable(x)
x = table2array(x);
end
% Group x into bins by using the
````discretize`

function.
xbinned = discretize(x,[-inf; edges{j}; inf]);
Xbinned(:,j) = xbinned;
end

`Xbinned`

contains the bin indices, ranging from 1 to the number of bins, for numeric predictors.
`Xbinned`

values are 0 for categorical predictors. If
`X`

contains `NaN`

s, then the corresponding
`Xbinned`

values are `NaN`

s.
`CategoricalPredictors`

— Indices of categorical predictors

vector of positive integers | `[]`

This property is read-only.

Categorical predictor
indices, specified as a vector of positive integers. `CategoricalPredictors`

contains index values indicating that the corresponding predictors are categorical. The index
values are between 1 and `p`

, where `p`

is the number of
predictors used to train the model. If none of the predictors are categorical, then this
property is empty (`[]`

).

**Data Types: **`single`

| `double`

`CombineWeights`

— How the ensemble combines weak learner weights

`'WeightedAverage'`

| `'WeightedSum'`

This property is read-only.

How the ensemble combines weak learner weights, returned as either
`'WeightedAverage'`

or `'WeightedSum'`

.

**Data Types: **`char`

`ExpandedPredictorNames`

— Expanded predictor names

cell array of character vectors

This property is read-only.

Expanded predictor names, returned as a cell array of character vectors.

If the model uses encoding for categorical variables, then
`ExpandedPredictorNames`

includes the names that describe the
expanded variables. Otherwise, `ExpandedPredictorNames`

is the same as
`PredictorNames`

.

**Data Types: **`cell`

`FitInfo`

— Fit information

numeric array

Fit information, returned as a numeric array. The `FitInfoDescription`

property describes the content of this array.

**Data Types: **`double`

`FitInfoDescription`

— Description of information in `FitInfo`

character vector | cell array of character vectors

Description of the information in `FitInfo`

, returned as a character vector or cell array of character vectors.

**Data Types: **`char`

| `cell`

`HyperparameterOptimizationResults`

— Description of cross-validation optimization of hyperparameters

`BayesianOptimization`

object | table of hyperparameters and associated values

This property is read-only.

Description of the cross-validation optimization of hyperparameters, returned as a
`BayesianOptimization`

object or a table of
hyperparameters and associated values. Nonempty when the
`OptimizeHyperparameters`

name-value pair is nonempty at creation.
Value depends on the setting of the `HyperparameterOptimizationOptions`

name-value pair at creation:

`'bayesopt'`

(default) — Object of class`BayesianOptimization`

`'gridsearch'`

or`'randomsearch'`

— Table of hyperparameters used, observed objective function values (cross-validation loss), and rank of observations from lowest (best) to highest (worst)

`LearnerNames`

— Names of weak learners in ensemble

cell array of character vectors

This property is read-only.

Names of weak learners in ensemble, returned as a cell array of character vectors. The
name of each learner appears just once. For example, if you have an ensemble of 100
trees, `LearnerNames`

is `{'Tree'}`

.

**Data Types: **`cell`

`Method`

— Method that creates ensemble

character vector

Method that `fitrensemble`

uses to create the ensemble, returned as a character vector.

**Data Types: **`char`

`ModelParameters`

— Parameters used in training ensemble

`EnsembleParams`

object

Parameters used in training the ensemble, returned as an `EnsembleParams`

object. The properties of `ModelParameters`

include the type of ensemble, either `'classification'`

or `'regression'`

, the `Method`

used to create the ensemble, and other parameters, depending on the ensemble.

`NumObservations`

— Number of observations in the training data

positive integer

This property is read-only.

Number of observations in the training data, returned as a positive integer.
`NumObservations`

can be less than the number of rows of input data
when there are missing values in the input data or response data.

**Data Types: **`double`

`NumTrained`

— Number of trained weak learners

positive integer

This property is read-only.

Number of trained weak learners in the ensemble, returned as a positive integer.

**Data Types: **`double`

`PredictorNames`

— Predictor names

cell array of character vectors

This property is read-only.

Predictor names, specified as a cell array of character vectors. The order of the
entries in `PredictorNames`

is the same as in the training data.

**Data Types: **`cell`

`ReasonForTermination`

— Reason that `fitrensemble`

stopped adding weak learners to the ensemble

character vector

This property is read-only.

Reason that `fitrensemble`

stopped adding weak learners to the ensemble, returned as a character vector.

**Data Types: **`char`

`Regularization`

— Result of using `regularize`

on ensemble

structure

Result of using the `regularize`

method on the ensemble, returned as a structure. Use `Regularization`

with `shrink`

to lower resubstitution error and shrink the ensemble.

**Data Types: **`struct`

`ResponseName`

— Name of the response variable

character vector

This property is read-only.

Name of the response variable, returned as a character vector.

**Data Types: **`char`

`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`

`Trained`

— Trained regression models

cell vector

Trained regression models, returned as a cell vector. The entries of the cell vector contain the corresponding compact regression models.

If `Method`

is `'LogitBoost'`

or `'GentleBoost'`

, then the ensemble stores trained learner `j`

in the `CompactRegressionLearner`

property of the object stored in `Trained{j}`

. That is, to access trained learner `j`

, use `ens.Trained{j}.CompactRegressionLearner`

.

**Data Types: **`cell`

`TrainedWeights`

— Trained weak learner weights

numeric vector

This property is read-only.

Trained weights for the weak learners in the ensemble, returned as a numeric vector.
`TrainedWeights`

has `T`

elements, where
`T`

is the number of weak learners in
`learners`

. The ensemble computes predicted response by aggregating
weighted predictions from its learners.

**Data Types: **`double`

`W`

— Scaled weights in tree

numeric vector

This property is read-only.

Scaled weights in `tree`

, returned as a numeric vector.
`W`

has length `n`

, the number of rows in the
training data.

**Data Types: **`double`

`X`

— Predictor values

real matrix | table

This property is read-only.

Predictor values, returned as a real matrix or table. Each column of
`X`

represents one variable (predictor), and each row represents
one observation.

**Data Types: **`double`

| `table`

`Y`

— Row classifications

categorical array | cell array of character vectors | character array | logical vector | numeric vector

This property is read-only.

Row classifications corresponding to the rows of `X`

, returned as a categorical array, cell array of character vectors, character array, logical vector, or a numeric vector. Each row of `Y`

represents the classification of the corresponding row of `X`

.

**Data Types: **`single`

| `double`

| `logical`

| `char`

| `string`

| `cell`

| `categorical`

## Object Functions

`compact` | Reduce size of regression ensemble model |

`crossval` | Cross-validate machine learning model |

`cvshrink` | Cross-validate pruning and regularization of regression ensemble |

`gather` | Gather properties of Statistics and Machine Learning Toolbox object from GPU |

`lime` | Local interpretable model-agnostic explanations (LIME) |

`loss` | Regression error for regression ensemble model |

`partialDependence` | Compute partial dependence |

`plotPartialDependence` | Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots |

`predict` | Predict responses using regression ensemble model |

`predictorImportance` | Estimates of predictor importance for regression ensemble of decision trees |

`regularize` | Find optimal weights for learners in regression ensemble |

`removeLearners` | Remove members of compact regression ensemble |

`resubLoss` | Resubstitution loss for regression ensemble model |

`resubPredict` | Predict response of regression ensemble by resubstitution |

`resume` | Resume training of regression ensemble model |

`shapley` | Shapley values |

`shrink` | Prune regression ensemble |

## Examples

### Train Boosted Regression Ensemble

Load the `carsmall`

data set. Consider a model that explains a car's fuel economy (`MPG`

) using its weight (`Weight`

) and number of cylinders (`Cylinders`

).

```
load carsmall
X = [Weight Cylinders];
Y = MPG;
```

Train a boosted ensemble of 100 regression trees using the `LSBoost`

method. Specify that `Cylinders`

is a categorical variable.

Mdl = fitrensemble(X,Y,'Method','LSBoost',... 'PredictorNames',{'W','C'},'CategoricalPredictors',2)

Mdl = RegressionEnsemble PredictorNames: {'W' 'C'} ResponseName: 'Y' CategoricalPredictors: 2 ResponseTransform: 'none' NumObservations: 94 NumTrained: 100 Method: 'LSBoost' LearnerNames: {'Tree'} ReasonForTermination: 'Terminated normally after completing the requested number of training cycles.' FitInfo: [100x1 double] FitInfoDescription: {2x1 cell} Regularization: []

`Mdl`

is a `RegressionEnsemble`

model object that contains the training data, among other things.

`Mdl.Trained`

is the property that stores a 100-by-1 cell vector of the trained regression trees (`CompactRegressionTree`

model objects) that compose the ensemble.

Plot a graph of the first trained regression tree.

view(Mdl.Trained{1},'Mode','graph')

By default, `fitrensemble`

grows shallow trees for boosted ensembles of trees.

Predict the fuel economy of 4,000 pound cars with 4, 6, and 8 cylinders.

XNew = [4000*ones(3,1) [4; 6; 8]]; mpgNew = predict(Mdl,XNew)

`mpgNew = `*3×1*
19.5926
18.6388
15.4810

## Tips

For an ensemble of regression trees, the `Trained`

property
contains a cell vector of `ens.NumTrained`

`CompactRegressionTree`

model objects. For a textual or graphical display of
tree * t* in the cell vector,
enter

view(ens.Trained{t})

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The

`predict`

function supports code generation.To integrate the prediction of an ensemble into Simulink

^{®}, you can use the RegressionEnsemble Predict block in the Statistics and Machine Learning Toolbox™ library or a MATLAB^{®}Function block with the`predict`

function.When you train an ensemble by using

`fitrensemble`

, the following restrictions apply.The value of the

`ResponseTransform`

name-value argument cannot be an anonymous function.Code generation limitations for regression trees also apply to ensembles of regression trees. You cannot use surrogate splits; that is, the value of the

`Surrogate`

name-value argument must be`'off'`

.

For fixed-point code generation, the following additional restrictions apply.

When you train an ensemble by using

`fitrensemble`

, the value of the`ResponseTransform`

name-value argument must be`'none'`

(default).Categorical predictors (

`logical`

,`categorical`

,`char`

,`string`

, or`cell`

) are not supported. You cannot use the`CategoricalPredictors`

name-value argument. To include categorical predictors in a model, preprocess them by using`dummyvar`

before fitting the model.

For more information, see Introduction to Code Generation.

### GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

The following object functions fully support GPU arrays:

The following object functions offer limited support for GPU arrays:

The object functions execute on a GPU if any of the following apply:

The model was fitted with GPU arrays.

The predictor data that you pass to the object function is a GPU array.

The response data that you pass to the object function is a GPU array.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

## Version History

**Introduced in R2011a**

## See Also

`ClassificationEnsemble`

| `fitrensemble`

| `CompactRegressionEnsemble`

| `templateTree`

| `view`

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