loss

Regression error for regression ensemble model

Syntax

L = loss(ens,tbl,ResponseVarName)

L = loss(ens,tbl,ResponseVarName)

L = loss(ens,tbl,Y)

L = loss(ens,X,Y)

L = loss(___,Name=Value)

Description

L = loss(ens,tbl,ResponseVarName) returns the mean squared error Lbetween the predictions of ens to the data in tbl, compared to the true responses tbl.ResponseVarName. The interpretation of L depends on the loss function (LossFun) and weighting scheme (Weights). In general, better classifiers yield smaller classification loss values. The formula for loss is described in the section Weighted Mean Squared Error.

L = loss(ens,tbl,ResponseVarName) returns the Classification Loss L for the trained classification ensemble model ens using the predictor data in table tbl and the true class labels in tbl.ResponseVarName.

L = loss(ens,tbl,Y) returns the mean squared error between the predictions of ens to the data in tbl, compared to the true responses Y.

L = loss(ens,X,Y) returns the mean squared error between the predictions of ens to the data in X, compared to the true responses Y.

L = loss(___,Name=Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in the previous syntaxes. For example, you can specify the loss function, the aggregation level for output, and whether to perform calculations in parallel.

Examples

Find Mean-Squared Error of Ensemble Predictions

Find the loss of an ensemble predictor using the carsmall data set.

Load the carsmall data set and select engine displacement, horsepower, and vehicle weight as predictors.

load carsmall
X = [Displacement Horsepower Weight];

Train an ensemble of regression trees and find the regression error for predicting MPG.

ens = fitrensemble(X,MPG);
L = loss(ens,X,MPG)

L = 
0.3463

Input Arguments

ens — Regression ensemble model

RegressionEnsemble model object | RegressionBaggedEnsemble model object | CompactRegressionEnsemble model object

Regression ensemble model, specified as a RegressionEnsemble or RegressionBaggedEnsemble model object trained with fitrensemble, or a CompactRegressionEnsemble model object created with compact.

tbl — Sample data

table

Sample data, specified as a table. Each row of tbl corresponds to one observation, and each column corresponds to one predictor variable. tbl must contain all of the predictors used to train the model. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

If you trained ens using sample data contained in a table, then the input data for loss must also be in a table.

Data Types: table

ResponseVarName — Response variable name

name of variable in tbl

Response variable name, specified as the name of a variable in tbl. The response variable must be a numeric vector.

You must specify ResponseVarName as a character vector or string scalar. For example, if the response variable Y is stored as tbl.Y, then specify it as "Y". Otherwise, the software treats all columns of tbl, including Y, as predictors.

Data Types: char | string

Y — Response data

numeric column vector

Response data, specified as a numeric column vector with the same number of rows as tbl or X. Each entry in Y is the true response to the data in the corresponding row of tbl or X.

The software treats NaN values in Y as missing values. Observations with missing values for Y are not used in the loss calculation.

Data Types: double | single

X — Predictor data

numeric matrix

Predictor data, specified as a numeric matrix.

Each row of X corresponds to one observation, and each column corresponds to one variable. The variables in the columns of X must be the same as the variables used to train ens.

The number of rows in X must equal the number of rows in Y.

If you trained ens using sample data contained in a matrix, then the input data for loss must also be in a matrix.

Data Types: double | single

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: loss(Mdl,X,Learners=[1 2 4],UseParallel=true) specifies to use the first, second, and fourth weak learners in the ensemble, and to perform computations in parallel.

Learners — Indices of weak learners

[1:ens.NumTrained] (default) | vector of positive integers

Indices of the weak learners in the ensemble to use with loss, specified as a vector of positive integers in the range [1:ens.NumTrained]. By default, the function uses all learners.

Example: Learners=[1 2 4]

Data Types: single | double

LossFun — Loss function

"mse" (default) | function handle

Loss function, specified as "mse" (mean squared error) or as a function handle. If you pass a function handle fun, loss calls it as

fun(Y,Yfit,W)

where Y, Yfit, and W are numeric vectors of the same length.

• Y is the observed response.

• Yfit is the predicted response.

• W is the observation weights.

The returned value of fun(Y,Yfit,W) must be a scalar.

Example: LossFun="mse"

Example: LossFun=@Lossfun

Data Types: char | string | function_handle

Mode — Aggregation level for output

"ensemble" (default) | "individual" | "cumulative"

Aggregation level for the output, specified as "ensemble", "individual", or "cumulative".

Value	Description
"ensemble"	The output is a scalar value, the loss for the entire ensemble.
"individual"	The output is a vector with one element per trained learner.
"cumulative"	The output is a vector in which element J is obtained by using learners 1:J from the input list of learners.

Example: Mode="individual"

Data Types: char | string

UseObsForLearner — Use observations for learner

true(N,NumTrained) (default) | logical matrix

Logical matrix of size N-by-NumTrained, where N is the number of observations in ens.X, and NumTrained is the number of weak learners. When UseObsForLearner(i,j) is true (default), learner j is used in predicting the response of row i of X.

Data Types: logical matrix

UseParallel — Flag to run in parallel

false or 0 (default) | true or 1

Flag to run in parallel, specified as a numeric or logical 1 (true) or 0 (false). If you specify UseParallel=true, the loss function executes for-loop iterations by using parfor. The loop runs in parallel when you have Parallel Computing Toolbox™.

Example: UseParallel=true

Data Types: logical

Weights — Observation weights

ones(size(X,1),1) (default) | numeric vector | name of variable in tbl

Observation weights, specified as a numeric vector or the name of a variable in tbl. The software weighs the observations in each row of X or tbl with the corresponding weight in Weights. The formula for loss with Weights is described in the section Weighted Mean Squared Error.

If you specify Weights as a numeric vector, then the size of Weights must be equal to the number of rows in X or tbl.

If you specify Weights as the name of a variable in tbl, you must do so as a character vector or string scalar. For example, if the weights are stored as tbl.W, then specify Weights as "W". Otherwise, the software treats all columns of Tbl, including tbl.W, as predictors.

If you do not specify your own loss function, then the software normalizes Weights to sum up to the value of the prior probability in the respective class.

Example: Weights="W"

Data Types: single | double | char | string

More About

Weighted Mean Squared Error

Let n be the number of rows of data, x_j be the jth row of data, y_j be the true response to x_j, and let f(x_j) be the response prediction of ens to x_j. Let w be the vector of weights (all one by default).

First the weights are divided by their sum so they add to one: w→w/Σw. The mean squared error L is

$$L={\displaystyle \sum _{j=1}^n{w}_j{\left(f\left(x_j\right)-y_j\right)}^2}.$$

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

Usage notes and limitations:

• You cannot use the UseParallel name-value argument with tall arrays.

For more information, see Tall Arrays.

Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

To run in parallel, set the UseParallel name-value argument to true in the call to this function.

For more general information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).

You cannot use the UseParallel name-value argument with tall arrays, GPU arrays, or code generation.

GPU Arrays

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

Usage notes and limitations:

• The loss function does not support ensembles trained using decision tree learners with surrogate splits.

• You cannot use UseParallel with GPU arrays.

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

Version History

Introduced in R2011a