# oobLoss

Out-of-bag error for bagged regression ensemble model

## Syntax

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

## Description

example

````L = oobLoss(ens)` returns the mean squared error `L` for the out-of-bag data in the bagged regression ensemble model `ens`. The interpretation of `L` depends on the loss function (`LossFun`). In general, better classifiers yield smaller classification loss values.```
````L = oobLoss(ens,Name=Value)` specifies additional options using one or more name-value arguments. For example, you can specify the indices of the weak learners to use for calculating the error, the aggregation level for the output, and to perform computations in parallel.```

## Examples

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

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 bagged regression trees.

`ens = fitrensemble(X,MPG,'Method','Bag');`

Find the out-of-bag error.

`L = oobLoss(ens)`
```L = 16.9551 ```

## Input Arguments

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Bagged regression ensemble model, specified as a `RegressionBaggedEnsemble` model object trained with `fitrensemble`.

### 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: `oobLoss(ens,Learners=[1 2 3 5],UseParallel=true)` specifies to use the first, second, third, and fifth learners in the ensemble in `oobLoss`, and to perform computations in parallel.

Indices of weak learners in the ensemble to use in `oobLoss`, specified as a vector of positive integers in the range [1:`ens.NumTrained`]. By default, all learners are used.

Example: `Learners=[1 2 4]`

Data Types: `single` | `double`

Loss function, specified as `"mse"` (mean squared error) or as a function handle. 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.

• `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`

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

ValueDescription
`"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`

Flag to run in parallel, specified as a numeric or logical 1 (`true`) or 0 (`false`). If you specify `UseParallel=true`, the `oobLoss` 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`

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### 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, `fitrensemble` generates many bootstrap replicas of the dataset and grows decision trees on these replicas. `fitrensemble` 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` takes 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.

## Version History

Introduced in R2012b