# SelectByTargetMeanPerformance#

`SelectByTargetMeanPerformance()`

selects features based on performance metrics
like the ROC-AUC or accuracy for classification, or mean squared error and R-squared
for regression.

To obtain performance metrics, we compare an estimate of the target, returned by a machine learning model, with the real target. The closer the values of the estimate to the real target, the better the performance of the model.

`SelectByTargetMeanPerformance()`

, like `SelectBySingleFeaturePerformance()`

train models based on single features. Or in other words, they train and test one model
per feature. With `SelectBySingleFeaturePerformance()`

, we can use any machine
learning classifier or regressor available in Scikit-learn to evaluate each feature’s
performance. The downside is that Scikit-learn models only work with numerical variables,
thus, if our data has categorical variables, we need to encode them into numbers first.

`SelectByTargetMeanPerformance()`

, on the other hand, can select both numerical
and categorical variables. `SelectByTargetMeanPerformance()`

uses a very simple
“machine learning model” to estimate the target. It estimates the target by returning
the mean target value per category or per interval. And with this prediction, it
determines a performance metric for each feature.

These feature selection idea is very simple; it involves taking the mean of the responses (target) for each level (category or interval), and so amounts to a least squares fit on a single categorical variable against a response variable, with the categories in the continuous variables defined by intervals.

`SelectByTargetMeanPerformance()`

works with cross-validation. It uses the k-1
folds to define the numerical intervals and learn the mean target value per category or
interval. Then, it uses the remaining fold to evaluate the performance of the
feature: that is, in the last fold it sorts numerical variables into the bins, replaces
bins and categories by the learned target estimates, and calculates the performance of
each feature.

Despite its simplicity, the method has a number of advantages:

Speed: Computing means and intervals is fast, straightforward and efficient.

Stability with respect to feature magnitude: Extreme values for continuous variables do not skew predictions as they would in many models.

Comparability between continuous and categorical variables.

Accommodation of non-linearities.

Does not require encoding categorical variables into numbers.

The method has also some limitations. First, the selection of the number of intervals as well as the threshold is arbitrary. And also, rare categories and very skewed variables will raise errors when NAN are accidentally introduced during the evaluation.

## Important#

`SelectByTargetMeanPerformance()`

automatically identifies numerical and
categorical variables. It will select as categorical variables, those cast as object
or categorical, and as numerical variables those of type numeric. Therefore, make sure
that your variables are of the correct data type.

## Troubleshooting#

The main problem that you may encounter using this selector is having missing data introduced in the variables when replacing the categories or the intervals by the target mean estimates.

### Categorical variables#

NAN are introduced in categorical variables when a category present in the kth fold was not present in the k-1 fold used to calculate the mean target value per category. This is probably due to the categorical variable having high cardinality (a lot of categories) or rare categories, that is, categories present in a small fraction of the observations.

If this happens, try reducing the cardinality of the variable, for example by grouping rare labels into a single group. Check the RareLabelEncoder for more details.

### Numerical variables#

NAN are introduced in numerical variables when an interval present in the kth cross-validation fold was not present in the k-1 fold used to calculate the mean target value per interval. This is probably due to the numerical variable being highly skewed, or having few unique values, for example, if the variable is discrete instead of continuous.

If this happens, check the distribution of the problematic variable and try to identify the problem. Try using equal-frequency intervals instead of equal-width and also reducing the number of bins.

If the variable is discrete and has few unique values, another thing you could do is casting the variable as object, so that the selector evaluates the mean target value per unique value.

Finally, if a numerical variable is truly continuous and not skewed, check that it is not accidentally cast as object.

## Example#

Let’s see how to use this method to select variables in the Titanic dataset. This data has a mix of numerical and categorical variables, then it is a good option to showcase this selector.

Let’s import the required libraries and classes, and prepare the titanic dataset:

```
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from feature_engine.datasets import load_titanic
from feature_engine.encoding import RareLabelEncoder
from feature_engine.selection import SelectByTargetMeanPerformance
data = load_titanic(
handle_missing=True,
predictors_only=True,
cabin="letter_only",
)
# replace infrequent cabins by N
data['cabin'] = np.where(data['cabin'].isin(['T', 'G']), 'N', data['cabin'])
# cap maximum values
data['parch'] = np.where(data['parch']>3,3,data['parch'])
data['sibsp'] = np.where(data['sibsp']>3,3,data['sibsp'])
# cast variables as object to treat as categorical
data[['pclass','sibsp','parch']] = data[['pclass','sibsp','parch']].astype('O')
print(data.head())
```

We can see the first 5 rows of data below:

```
pclass survived sex age sibsp parch fare cabin embarked
0 1 1 female 29.0000 0 0 211.3375 B S
1 1 1 male 0.9167 1 2 151.5500 C S
2 1 0 female 2.0000 1 2 151.5500 C S
3 1 0 male 30.0000 1 2 151.5500 C S
4 1 0 female 25.0000 1 2 151.5500 C S
```

Let’s now go ahead and split the data into train and test sets:

```
# separate train and test sets
X_train, X_test, y_train, y_test = train_test_split(
data.drop(['survived'], axis=1),
data['survived'],
test_size=0.1,
random_state=0)
X_train.shape, X_test.shape
```

We see the sizes of the datasets below:

```
((1178, 8), (131, 8))
```

Now, we set up `SelectByTargetMeanPerformance()`

. We will examine the roc-auc
using 3 fold cross-validation. We will separate numerical variables into equal-frequency
intervals. And we will retain those variables where the roc-auc is bigger than the mean
ROC-AUC of all features (default functionality).

```
sel = SelectByTargetMeanPerformance(
variables=None,
scoring="roc_auc",
threshold=None,
bins=3,
strategy="equal_frequency",
cv=3,
regression=False,
)
sel.fit(X_train, y_train)
```

With `fit()`

the transformer:

replaces categories by the target mean

sorts numerical variables into equal-frequency bins

replaces bins by the target mean

calculates the the roc-auc for each transformed variable

selects features which roc-auc bigger than the average

In the attribute `variables_`

we find the variables that were evaluated:

```
sel.variables_
```

```
['pclass', 'sex', 'age', 'sibsp', 'parch', 'fare', 'cabin', 'embarked']
```

In the attribute `features_to_drop_`

we find the variables that were not selected:

```
sel.features_to_drop_
```

```
['age', 'sibsp', 'parch', 'embarked']
```

In the attribute `feature_performance_`

we find the ROC-AUC for each feature. Remember
that this is the average ROC-AUC in each cross-validation fold:

```
sel.feature_performance_
```

```
{'pclass': 0.668151138112005,
'sex': 0.764831274819234,
'age': 0.535490029737471,
'sibsp': 0.5815934176199077,
'parch': 0.5721327969642238,
'fare': 0.6545985745474006,
'cabin': 0.630092526712033,
'embarked': 0.5765961846034091}
```

The mean ROC-AUC of all features is 0.62, we can calculate it as follows:

```
pd.Series(sel.feature_performance_).mean()
0.6229357428894605
```

So we can see that the transformer correclty selected the features with ROC-AUC above that value.

With `transform()`

we can go ahead and drop the features:

```
Xtr = sel.transform(X_test)
Xtr.head()
```

```
pclass sex fare cabin
1139 3 male 7.8958 M
533 2 female 21.0000 M
459 2 male 27.0000 M
1150 3 male 14.5000 M
393 2 male 31.5000 M
```

And finally, we can also obtain the names of the features in the final transformed data:

```
sel.get_feature_names_out()
```

```
['pclass', 'sex', 'fare', 'cabin']
```

### More details#

Check also:

All notebooks can be found in a dedicated repository.

For more details about this and other feature selection methods check out these resources:

Feature selection for machine learning, online course.