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

import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
from feature_engine.selection import SelectByTargetMeanPerformance:

Let’s now load and prepare the Titanic dataset:

# load data
data = pd.read_csv('https://www.openml.org/data/get_csv/16826755/phpMYEkMl')
data.drop(labels = ['name','boat', 'ticket','body', 'home.dest'], axis=1, inplace=True)
data = data.replace('?', np.nan)

data.dropna(subset=['embarked', 'fare'], inplace=True)
data['fare'] = data['fare'].astype('float')

data['age'] = data['age'].astype('float')
data['age'] = data['age'].fillna(data['age'].mean())

def get_first_cabin(row):
    try:
        return row.split()[0]
    except:
        return 'N'

data['cabin'] = data['cabin'].apply(get_first_cabin)

# extract cabin letter
data['cabin'] = data['cabin'].str[0]

# 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')

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:

((1175, 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': 0.6692917241015676,
 'sex': 0.7624307804352095,
 'age': 0.5406671434172395,
 'sibsp': 0.5669758659668949,
 'parch': 0.5741629417199435,
 'fare': 0.6555307060922498,
 'cabin': 0.6323342342595275,
 'embarked': 0.57348024722553}

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

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

0.6218592054022702

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
611       3    male   9.3500     N
414       2    male  21.0000     N
530       2    male  10.5000     N
1149      3  female   7.7208     N
944       3    male   7.8958     N

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.