# oobLoss

Class: RegressionBaggedEnsemble

Out-of-bag regression error

## Syntax

`L = oobLoss(ens)L = oobLoss(ens,Name,Value)`

## Description

`L = oobLoss(ens)` returns the mean squared error for `ens` computed for out-of-bag data.

`L = oobLoss(ens,Name,Value)` computes error with additional options specified by one or more `Name,Value` pair arguments. You can specify several name-value pair arguments in any order as `Name1,Value1,…,NameN,ValueN`.

## Input Arguments

 `ens` A regression bagged ensemble, constructed with `fitensemble`.

### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside single quotes (`' '`). You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

 `'learners'` Indices of weak learners in the ensemble ranging from `1` to `NumTrained`. `oobLoss` uses only these learners for calculating loss. Default: `1:NumTrained` `'lossfun'` Function handle for loss function, or the string `'mse'`, meaning mean squared error. If you pass a function handle `fun`, `oobLoss` 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, and `W` is the observation weights. Default: `'mse'` `'mode'` String representing the 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'`

## Output Arguments

 `L` Mean squared error of the out-of-bag observations, a scalar. `L` can be a vector, or can represent a different quantity, depending on the name-value settings.

## Definitions

### Out of Bag

Bagging, which stands for "bootstrap aggregation", is a type of ensemble learning. To bag a weak learner such as a decision tree on a dataset, `fitensemble` generates many bootstrap replicas of the dataset and grows decision trees on these replicas. `fitensemble` obtains each bootstrap replica by randomly selecting `N` observations out of `N` with replacement, where `N` is the dataset size. To find the predicted response of a trained ensemble, `predict` take an average over predictions from individual trees.

Drawing `N` out of `N` observations with replacement omits on average 37% (1/e) of observations for each decision tree. These are "out-of-bag" observations. For each observation, `oobLoss` estimates the out-of-bag prediction by averaging over predictions from all trees in the ensemble for which this observation is out of bag. It then compares the computed prediction against the true response for this observation. It calculates the out-of-bag error by comparing the out-of-bag predicted responses against the true responses for all observations used for training. This out-of-bag average is an unbiased estimator of the true ensemble error.

## Examples

Compute the out-of-bag error for the `carsmall` data:

```load carsmall X = [Displacement Horsepower Weight]; ens = fitensemble(X,MPG,'bag',100,'Tree',... 'type','regression'); L = oobLoss(ens) L = 17.0665```