loss

Regression error

Syntax

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 between the predictions of ens to the data in tbl, compared to the true responses 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) computes the error in prediction with additional options specified by one or more Name,Value pair arguments, using any of the previous syntaxes.

Input Arguments

ens	A regression ensemble created with fitrensemble, or the compact method.
tbl	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 this method must also be in a table.
ResponseVarName	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 when training the model.
X	A matrix of predictor values. Each column of X represents one variable, and each row represents one observation. If you trained ens using sample data contained in a matrix, then the input data for this method must also be in a matrix.
Y	A numeric column vector with the same number of rows as tbl or X. Each entry in Y is the response to the data in the corresponding row of tbl or X. NaN values in Y are taken to be missing values. Observations with missing values for Y are not used in the calculation of loss.

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.

learners	Indices of weak learners in the ensemble ranging from 1 to ens.NumTrained. loss uses only these learners for calculating loss. Default: 1:NumTrained
lossfun	Function handle for loss function, or 'mse', meaning mean squared error. 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 fun(Y,Yfit,W) should be a scalar. Default: 'mse'
mode	Meaning of the output L: 'ensemble' — L is a scalar value, the loss for the entire ensemble. 'individual' — L is a vector with one element per trained learner. 'cumulative' — L is a vector in which element J is obtained by using learners 1:J from the input list of learners. Default: 'ensemble'
UseObsForLearner	A 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, predict uses learner J in predicting observation I. Default: true(N,NumTrained)
UseParallel	Indication to perform inference in parallel, specified as false (compute serially) or true (compute in parallel). Parallel computation requires Parallel Computing Toolbox™. Parallel inference can be faster than serial inference, especially for large datasets. Parallel computation is supported only for tree learners. Default: false
weights	Numeric vector of observation weights with the same number of elements as Y. The formula for loss with weights is in Weighted Mean Squared Error. Default: ones(size(Y))

Output Arguments

L	Weighted mean squared error of predictions. The formula for loss is in Weighted Mean Squared Error.

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

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 UseParallel 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 UseParallel with tall or GPU arrays.

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).