Optimal Feature Removal An Interactive Guide

Why is Feature Selection Important?

Feature selection is a vital preprocessing step in machine learning. Its main goal is to identify and keep only the most relevant features from your dataset. This process offers several significant benefits:

• Enhances Model Efficacy: By removing irrelevant or redundant features, models can often achieve better predictive accuracy and generalize better to new, unseen data.
• Reduces Computational Overhead: Fewer features mean less data to process, leading to faster model training and prediction times. This is especially important for large datasets.
• Improves Model Interpretability: Models with fewer features are generally easier to understand and explain. It becomes clearer which factors are driving the predictions.
• Mitigates Overfitting: Redundant or irrelevant features can sometimes cause models to "memorize" the training data (overfit) rather than learning general patterns, leading to poor performance on new data.
• Addresses Multicollinearity: Specifically, removing highly correlated features (which provide similar information) helps stabilize model coefficients and makes it easier to understand the individual contribution of each feature.

Ultimately, effective feature selection leads to more efficient, robust, and understandable machine learning models.

Key Metric: Missing Data Proportion

The proportion of missing values in a feature is a direct indicator of its completeness and reliability. Features with a high percentage of missing data are generally less informative and can complicate model training, even if imputation techniques are used.

Calculation: For each feature, it's `(Number of Null/NaN values) / (Total number of rows)`.

In the composite removal score, a higher missing proportion makes a feature more likely to be removed, as it suggests lower data quality and reliability.

Illustrative example of missing data proportions for hypothetical features.

Key Metric: Feature-Target Relationship

The strength of a feature's relationship with the target variable is crucial. Features that strongly predict or associate with the target are more valuable. The specific statistical measure used depends on the data types of the feature and the target (e.g., Pearson correlation for numeric-numeric, ANOVA F-value for numeric-categorical, Mutual Information for mixed types).

After calculating the appropriate metric, its value (often the absolute value) is normalized. In the composite removal score, a stronger (higher) normalized relationship with the target makes a feature less likely to be removed.

Illustrative example of normalized target relationship scores.

Key Metric: Individual Predictive Power

This metric assesses how well a single feature, on its own, can predict the target variable. For classification tasks, this is often represented by the Lift Ratio, calculated from a simple model trained only on that feature. For regression tasks, R-squared from a simple linear regression can be used.

A higher lift (or R-squared) indicates greater individual predictive capability. In the composite removal score, higher normalized predictive power makes a feature less likely to be removed.

Illustrative example of normalized individual predictive power scores.

The Composite Removal Score

To make an informed decision about which feature to remove from a highly correlated group, individual scores (missing proportion, target correlation, predictive power) are combined into a single composite removal score. These individual scores are first normalized (typically to a 0-1 range).

The formula is structured as a weighted sum:

Where:

• Wmissing, Wcorr, Wlift are user-defined weights (summing to 1).
• Norm_Missing is the normalized missing proportion.
• (1 - Norm_Target_Corr) inverts the normalized target correlation (higher original correlation means lower contribution to removal score).
• (1 - Norm_Predictive_Power) inverts the normalized predictive power (higher original power means lower contribution to removal score).

A higher final Removal_Score indicates the feature is a better candidate for removal. The feature with the lowest score in a correlated group is kept.

The Algorithm in Action

The core logic is encapsulated in a Python function, `remove_correlated_features_optimal`. Here's a conceptual overview of its steps:

Python Function Snippet

The following is a condensed representation of the Python function structure.

import pandas as pd
import numpy as np
from sklearn.preprocessing import MinMaxScaler
from sklearn.linear_model import LogisticRegression, LinearRegression
from mlxtend.evaluate import lift_score
import networkx as nx

def remove_correlated_features_optimal(
    df: pd.DataFrame,
    target_column: str,
    corr_threshold: float = 0.9,
    missing_weight: float = 0.3,
    target_corr_weight: float = 0.4,
    lift_weight: float = 0.3,
) -> pd.DataFrame:
    """
    Removes highly correlated features based on a composite score.
    Considers missing proportion, target correlation, and predictive power.
    """
    df_copy = df.copy()
    features = [col for col in df_copy.columns if col != target_column]
    
    # --- 1. Calculate All Individual Feature Scores ---
    feature_scores = {}
    
    # Calculate missing proportion for each feature
    missing_props = df_copy[features].isna().mean()
    
    # Calculate target correlation for numerical features
    numerical_features = df_copy[features].select_dtypes(include=np.number).columns.tolist()
    target = df_copy[target_column]
    
    # Calculate lift score (predictive power) using logistic regression
    lift_scores = {}
    for col in numerical_features:
        try:
            model = LogisticRegression() if target.dtype == np.dtype('O') else LinearRegression()
            model.fit(df_copy[[col]].fillna(0), target)
            y_pred = model.predict(df_copy[[col]].fillna(0))
            lift_scores[col] = lift_score(target, y_pred)
        except:
            lift_scores[col] = 0
    
    # Gather all scores
    for col in features:
        try:
            missing_prop = missing_props[col]
            target_corr = np.abs(df_copy[[col, target_column]].dropna().corr().iloc[0, 1]) if col in numerical_features else 0
            pred_power = lift_scores.get(col, 0)
            
            feature_scores[col] = {
                'missing_prop': missing_prop,
                'target_corr': target_corr,
                'pred_power': pred_power
            }
        except:
            feature_scores[col] = {
                'missing_prop': 1,
                'target_corr': 0,
                'pred_power': 0
            }
    
    # Normalize scores globally
    missing_vals = np.array([score['missing_prop'] for score in feature_scores.values()])
    target_corr_vals = np.array([score['target_corr'] for score in feature_scores.values()])
    pred_power_vals = np.array([score['pred_power'] for score in feature_scores.values()])
    
    scaler = MinMaxScaler()
    missing_vals_norm = scaler.fit_transform(missing_vals.reshape(-1, 1)).flatten()
    target_corr_vals_norm = scaler.fit_transform(target_corr_vals.reshape(-1, 1)).flatten()
    pred_power_vals_norm = scaler.fit_transform(pred_power_vals.reshape(-1, 1)).flatten()
    
    # --- 2. Identifying and Grouping Correlated Features ---
    corr_matrix = df_copy[numerical_features].corr().abs()
    G = nx.Graph()
    
    # Build graph based on correlation matrix
    for i in range(len(corr_matrix)):
        for j in range(i+1, len(corr_matrix)):
            if corr_matrix.iloc[i, j] > corr_threshold:
                G.add_edge(corr_matrix.index[i], corr_matrix.index[j])
    
    correlated_groups = list(nx.connected_components(G))
    
    # --- 3. Applying the Composite Score within Correlated Groups ---
    features_to_drop = set()
    
    for group in correlated_groups:
        if len(group) <= 1:
            continue
        group_feature_data = []
        
        # Get normalized scores for features in this group
        for feature in group:
            norm_missing = missing_vals_norm[[col == feature for col in features]]
            norm_target_corr = target_corr_vals_norm[[col == feature for col in features]]
            norm_pred_power = pred_power_vals_norm[[col == feature for col in features]]
            
            composite_score = (
                missing_weight * norm_missing +
                target_corr_weight * (1 - norm_target_corr) +
                lift_weight * (1 - norm_pred_power)
            )
            
            group_feature_data.append({'name': feature, 'score': composite_score[0]})  # Fixed indexing
            
        # Sort features by composite score and drop all but the best one
        sorted_group = sorted(group_feature_data, key=lambda x: x['score'])
        features_to_drop.update([f['name'] for f in sorted_group[1:]])
    
    final_df = df_copy.drop(columns=list(features_to_drop))
    return final_df

Interactive Explorer

Experiment with how the composite score changes for two hypothetical correlated features. Adjust their scores and the weights (using sliders in "The Composite Score" section) to see which feature would be kept.

For simplicity in this demo, input scores between 0 and 1 for Missing Proportion, Target Correlation, and Predictive Power. A higher Missing Proportion is worse, while higher Target Correlation and Predictive Power are better.

Advanced Considerations & Best Practices

To make the most of this feature removal approach, consider these points:

• Performance Optimization: For very large datasets, calculating predictive power for each feature can be slow. Consider using vectorized operations, sampling, or tools like Numba/Cython if performance is critical.
• Sensitivity Analysis & Threshold Tuning: The `corr_threshold` for grouping features and the weights for the composite score are key hyperparameters. Experiment with different values and use cross-validation to assess their impact on your specific model and data. There's no one-size-fits-all.
• Handling Edge Cases: Be mindful of features with zero variance (constant values), as they can cause issues in calculations. The function should ideally handle these by assigning default scores. Also, consider how non-numeric data (like dates or free text) is handled; they might need preprocessing or exclusion.
• Outliers: Extreme outliers can affect Pearson correlation and Min-Max scaling. If your data has significant outliers, explore robust scaling methods or outlier treatment before applying this function.
• Data Understanding: Always start with a thorough understanding of your dataset—feature distributions, potential issues, and the nature of your target variable. This context is vital for interpreting the results of any automated feature selection process.

Conclusion & Recommendations

The multi-criteria approach for removing highly correlated features offers a more data-driven and nuanced solution than simpler methods. By considering missingness, target relevance, and individual predictive power, it aims to retain the most valuable features within correlated groups.

Key recommendations for practitioners include:

• Understand Your Data: Deeply analyze your dataset before applying any automated selection.
• Experiment with Parameters: Tune the correlation threshold and score weights to fit your specific project needs.
• Integrate into a Pipeline: Use this as an early preprocessing step in your machine learning workflow.

Future enhancements could involve more advanced imputation, alternative predictive power metrics, or even integrating model-based feature importance for a hybrid approach.

This interactive guide aimed to provide a clear understanding of this optimal feature removal strategy. We hope it empowers you to build better, more efficient machine learning models!