Machine Learning Interview Question

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Machine Learning Interview Question - Feature Selection

Feature selection is a foundational task in any machine learning pipeline. The choice of features can dramatically impact the predictive power of your models, affect interpretability, and even reduce computation. One common interview question for data scientists is:

Data Science Interview Question:

Suggest some better feature selection technique than that of correlation.

You can definitely use PPS.

Why Feature Selection Matters in Machine Learning

Feature selection is the process of identifying and selecting the most relevant variables from your dataset to use as inputs in your model. Proper feature selection can:

Reduce model complexity and overfitting
Improve model accuracy and generalization
Decrease training time and resource usage
Enhance model interpretability

Selecting the right features ensures your machine learning models are efficient and robust, especially when dealing with high-dimensional data.

Traditional Feature Selection: The Role and Limitations of Correlation

Correlation, especially Pearson correlation coefficient, is a widely used metric for feature selection, particularly for identifying relationships between numerical variables. The Pearson correlation coefficient between variables \( X \) and \( Y \) is given by:

\[ \rho_{X,Y} = \frac{\mathrm{Cov}(X, Y)}{\sigma_X \sigma_Y} \]

where \( \mathrm{Cov}(X, Y) \) is the covariance and \( \sigma_X, \sigma_Y \) are the standard deviations of \( X \) and \( Y \).

Limitations of Correlation as a Feature Selection Tool

Linear Relationships Only: Pearson correlation measures only linear relationships. Non-linear associations are missed.
Symmetry: Correlation is symmetric (\( \rho_{X,Y} = \rho_{Y,X} \)), ignoring directionality, which is important for predictive tasks.
Data Types: It is defined only for numerical variables, making it less useful for categorical or mixed data.
Insensitive to Complex Dependencies: Fails to detect complex, non-linear, or interaction-based predictive relationships.

Given these limitations, relying solely on correlation can cause you to overlook powerful non-linear features or relationships in your data.

Advanced Feature Selection: Introducing Predictive Power Score (PPS)

A more modern, robust alternative to correlation is the Predictive Power Score (PPS). PPS is a data-type agnostic, model-based score that measures the predictive strength of one feature for another. It is designed to uncover both linear and non-linear relationships, work with numerical and categorical data, and capture the directionality of prediction.

What is Predictive Power Score (PPS)?

The Predictive Power Score (PPS) answers the question: How well can one feature predict another? PPS is calculated by training a simple machine learning model (like decision trees) to predict the target feature from the predictor, and then evaluating the predictive performance.

PPS returns a score between 0 and 1:

0: The predictor has no predictive power for the target.
1: The predictor perfectly predicts the target.

Key Advantages of PPS

Non-linear Relationships: Detects both linear and non-linear patterns between features.
Works with All Data Types: Equally effective for numerical, categorical, or mixed variables.
Asymmetric: \( \mathrm{PPS}(X, Y) \neq \mathrm{PPS}(Y, X) \), making it ideal for feature selection and predictive modeling.
Model-Agnostic: Uses machine learning under-the-hood, but the interface is simple and consistent.
Standardized: Output is always scaled between 0 and 1 for easy interpretation and comparison.

How is PPS Calculated?

PPS is calculated by training a simple machine learning model (typically a decision tree) to predict the target variable \( Y \) using the predictor variable \( X \). The predictive power is measured using suitable error metrics for classification or regression.

The general steps are:

For each pair \((X, Y)\), train a ML model to predict \( Y \) from \( X \).
Compute the model error (\( E_{\text{model}} \)).
Compute the baseline error (\( E_{\text{baseline}} \)), usually by always predicting the mean/mode.
Calculate the PPS as:
\[ \text{PPS} = \begin{cases} 0, & \text{if } E_{\text{model}} \geq E_{\text{baseline}} \\ 1 - \frac{E_{\text{model}}}{E_{\text{baseline}}}, & \text{otherwise} \end{cases} \]

This formula ensures that PPS is 0 if the model can’t beat the baseline, and approaches 1 as prediction becomes perfect.

PPS vs. Correlation: A Practical Comparison

Let’s compare PPS and correlation with some illustrative scenarios:

Linear Relationship: Both correlation and PPS will be high.
Non-linear Relationship: Correlation may be near zero, but PPS can be high if the predictor is useful.
Mixed Data Types: Correlation is undefined, but PPS works seamlessly.
Directionality: Correlation is symmetric; PPS distinguishes between \( X \rightarrow Y \) and \( Y \rightarrow X \).

Example: Non-linear Relationship


import numpy as np
import pandas as pd
from ppscore import score

# Generate non-linear data
df = pd.DataFrame({
    'x': np.linspace(-10, 10, 1000)
})
df['y'] = np.square(df['x'])  # y = x^2

# Pearson correlation
corr = df['x'].corr(df['y'])
print(f"Pearson Correlation: {corr:.3f}")

# PPS
pps = score(df, 'x', 'y')['ppscore']
print(f"PPS: {pps:.3f}")

In this case, the correlation is near zero (since squaring is symmetric), but PPS will be high, showing that x can predict y well.

Using PPS for Feature Selection: Step-by-Step

Let’s walk through a practical workflow for using PPS in feature selection.

1. Install PPS-Score Python Package


pip install ppscore

2. Calculate PPS Matrix

The ppscore.pps_matrix function computes the PPS for all pairs of columns in your DataFrame.


import ppscore as pps
import pandas as pd

# Example DataFrame df
pps_matrix = pps.matrix(df)
print(pps_matrix)

This produces a matrix where each cell \((i, j)\) contains the PPS for feature \(i\) predicting feature \(j\).

3. Select Top Features for Target Variable

To select the best predictors for your target, filter the PPS matrix for the column where y is the target:


target_variable = 'y'
feature_scores = pps.predictors(df, target_variable)
# Sort features by PPS descending
top_features = feature_scores.sort_values(by='ppscore', ascending=False)
print(top_features)

4. Set a PPS Threshold

You can select all features with a PPS above a certain threshold (e.g., 0.05 or 0.1) to include in your model.


selected_features = top_features[top_features['ppscore'] > 0.1]['x']
print(selected_features)

Comparing PPS with Other Feature Selection Techniques

While PPS is powerful, it is one tool in your feature selection toolkit. Let’s compare it with other common methods.

1. Filter Methods

Correlation: As discussed, limited to linear, numerical data.
Mutual Information: Measures any dependency, but is symmetric and can be harder to interpret.
Chi-Square Test: For categorical data, but assumes independence.

2. Wrapper Methods

Recursive Feature Elimination (RFE): Repeatedly builds models and removes the weakest features. Computationally expensive.
Forward/Backward Selection: Sequentially adds/removes features based on model performance.

3. Embedded Methods

Regularization (Lasso/Ridge): Selects features by penalizing coefficients during training.
Tree-based Feature Importance: Uses splits in decision trees to determine importance.

How PPS Stands Out

Versatility: Handles all data types and relationships elegantly.
Speed: Faster than wrapper methods, as it only trains simple models per feature.
Interpretability: Provides standardized, directional scores for each predictor-target pair.

Best Practices for Using PPS in Feature Selection

Combine with Domain Knowledge: Use PPS to guide selection, but always consider business context and interpretability.
Avoid Multicollinearity: PPS doesn’t detect collinearity among predictors. After initial selection, check for highly correlated features.
Iterative Approach: Use PPS in combination with recursive feature elimination or tree-based methods for best results.
Threshold Tuning: Experiment with different PPS thresholds to control model complexity.
Model-Agnostic: Since PPS doesn’t depend on the final model type, it is useful in the early data exploration stage.

When Not to Use PPS

While PPS is robust, it is not always a silver bullet. Avoid using PPS:

For very high-dimensional datasets (thousands of features), as computing PPS for all pairs can be slow.
When interpretability of the relationship type (linear vs. non-linear) is crucial for your application.
If your target is time-series or sequence data where autocorrelation and order matter.

In such cases, consider combining PPS with other techniques or using domain-specific methods.

Complementary Techniques: Enriching Feature Selection

PPS is a powerful addition to your toolbox, but the best results come from combining multiple approaches:

PPS + Correlation: PPS for initial selection, correlation to remove highly collinear predictors.
PPS + Tree Feature Importance: PPS to shortlist features, then use Random Forest or Gradient Boosting to refine with model-based importance.
PPS + Regularization: PPS for exploratory filtering, Lasso for embedded selection during model training.

Case Study: Using PPS for Feature Selection in a Real Dataset

Let’s demonstrate PPS-based feature selection on the classic Titanic dataset:


import pandas as pd
import ppscore as pps

# Load the Titanic dataset
df = pd.read_csv('titanic.csv')

# Calculate PPS for all features predicting 'Survived'
feature_scores = pps.predictors(df, 'Survived')
print(feature_scores.sort_values(by='ppscore', ascending=False))

Sample output might be:


    x        y      ppscore
0  Sex  Survived     0.53
1  Pclass Survived   0.21
2  Age   Survived    0.14
3  Fare  Survived    0.09
4  Embarked Survived 0.03

This suggests Sex is the most predictive feature for survival, followed by Pclass and Age. You can then use these features for model building.

Interview Answer: Suggesting PPS Over Correlation

In a machine learning interview, if asked for a better feature selection technique than correlation, you can answer:

“While correlation is a good starting point for identifying linear relationships among numerical features, it misses non-linear, categorical, and directional relationships. I recommend using the Predictive Power Score (PPS), which measures how well one feature predicts another, regardless of data type or relationship form. PPS is asymmetric and detects both linear and complex non-linear patterns, making it a versatile, model-agnostic feature selection tool for modern datasets. For example, in a dataset with both numerical and categorical features, PPS can uncover surprising predictive relationships that correlation would miss.”

Common Follow-Up Interview Questions

How does PPS differ from Mutual Information?
While both measure dependency, mutual information is symmetric and harder to interpret directionally, whereas PPS is asymmetric and directly interpretable as predictive strength.
Can PPS be used with time-series or sequence data?
PPS is not designed for time-dependent relationships; use lag features, autocorrelation, or specialized models for such data.

How do you handle multicollinearity after using PPS? After using PPS to select features, it's important to ensure that your final set of predictors is not highly collinear. High multicollinearity can destabilize coefficients in models like linear regression and inflate variance. To address this:

Calculate Pairwise Correlation: After selecting features with high PPS, compute the correlation matrix among those features. Remove one of any pair of features with a high absolute correlation (commonly, above 0.8).
Variance Inflation Factor (VIF): For regression models, calculate VIF for each predictor. Drop features with VIF values larger than 5 or 10.

This two-step approach—PPS for predictive relevance, correlation/VIF for redundancy—yields a compact, non-redundant set of features.

PPS in Practice: Additional Tips and Tricks

To get the most out of PPS in real-world feature selection, consider these tips:

Handling Missing Data: PPS will ignore missing values by default. However, excessive missingness can reduce the reliability of the PPS score. Impute missing values or use missing indicators if necessary.
Scaling and Encoding: PPS does not require manual scaling or encoding; it handles categorical and numerical variables natively. However, rare categories with very few samples might lead to unstable scores.
Computational Cost: For wide datasets, computing the full PPS matrix can be slow. Limit PPS calculation to features with reasonable prior importance or use parallel processing.
Interpretation: Remember that a high PPS does not guarantee causation—it simply indicates predictive association.

Frequently Asked Questions about PPS and Feature Selection

1. Is PPS affected by overfitting?

PPS uses simple models (typically shallow decision trees) and cross-validation to avoid overfitting. However, in very small datasets, overfitting is still possible, so interpret scores with caution.

2. Can PPS be used for unsupervised tasks?

No. PPS is designed to measure predictive power between features, which requires a target variable. For unsupervised tasks like clustering, use mutual information or dimensionality reduction techniques.

3. How do I choose a PPS threshold?

There is no universal threshold. Common practice is to plot the distribution of PPS scores and select a cutoff (e.g., 0.05, 0.1, or based on the "elbow" in the plot) that balances predictive power and model simplicity.

4. Is PPS available in R or other languages?

While PPS is most popular as a Python package (ppscore), there is also an R implementation and the logic can be ported to other languages with decision tree libraries.

Advanced Feature Selection Strategies Using PPS

For complex datasets, consider integrating PPS in more advanced feature selection strategies:

1. PPS and Feature Engineering

After an initial round of feature selection, create new features (interactions, polynomials, groupings), then re-calculate PPS to discover which engineered features add predictive value.

2. PPS with Ensemble Methods

Use PPS to select a reasonable subset of features, then apply tree-based ensemble methods (Random Forest, XGBoost) and extract their feature importances for final selection.

3. PPS for Automated Machine Learning (AutoML)

PPS is a fast, model-agnostic filter step for automated pipelines, reducing the search space for more computationally expensive model selection and hyperparameter tuning.

Limitations and Potential Pitfalls of PPS

Only Univariate Selection: PPS evaluates features one at a time. It does not capture multi-feature interactions unless you explicitly create interaction features.
Computational Cost: For datasets with thousands of features, computing the full PPS matrix may be slow.
Not Causal: High PPS implies prediction, not causation. Always supplement with domain knowledge.
Model Choice Sensitivity: The underlying model (usually decision trees) might not capture all patterns for some data types (e.g., time series, text).

PPS vs. Mutual Information: A Closer Look

Both PPS and mutual information (MI) detect non-linear, potentially complex relationships. Here’s how they differ:

Symmetry: MI is symmetric (\( \text{MI}(X,Y) = \text{MI}(Y,X) \)), PPS is not (\( \text{PPS}(X,Y) \neq \text{PPS}(Y,X) \)).
Interpretability: PPS is always in [0,1], easy to interpret as "predictive power." MI is non-negative but unbounded, making it harder to compare across datasets.
Implementation: MI requires discretization of continuous variables or kernel estimation, which can introduce bias. PPS uses off-the-shelf decision trees.

In practice, PPS is often more actionable for predictive modeling tasks, especially when directionality matters.

Summary Table: PPS vs. Correlation vs. Mutual Information

Criterion	Correlation	Mutual Information	PPS
Linear/Non-linear	Linear only	Both	Both
Symmetric?	Yes	Yes	No
Handles Categorical Data	No	Yes	Yes
Standardized Scale	[-1, 1]	No	[0, 1]
Directionality	No	No	Yes
Model-Agnostic	Yes	Yes	Yes
Interpretability	Easy	Tricky	Easy

Real-World Applications of PPS-based Feature Selection

Customer Churn Prediction: Use PPS to uncover which behavioral or demographic features best predict customer churn, even if relationships are non-linear or involve categorical variables.
Credit Scoring: Identify which financial, behavioral, and transactional features most strongly predict default, regardless of data type.
Medical Diagnosis: Select symptoms, test results, and history features that have the strongest predictive power for specific diagnoses.
Fraud Detection: Detect non-obvious, non-linear relationships in transaction data that correlate with fraudulent activity.

PPS Feature Selection: End-to-End Example

Suppose you have a dataset for predicting housing prices. Here’s an end-to-end workflow:


import pandas as pd
import ppscore as pps

# Load your dataset
df = pd.read_csv('housing.csv')

# Calculate PPS for all features to predict 'price'
feature_scores = pps.predictors(df, 'price')
print(feature_scores.sort_values(by='ppscore', ascending=False))

# Select features with PPS > 0.1
selected = feature_scores[feature_scores['ppscore'] > 0.1]['x']
print(selected)

# Check for multicollinearity among selected features
corr_matrix = df[selected].corr().abs()
upper = corr_matrix.where(np.triu(np.ones(corr_matrix.shape), k=1).astype(bool))
to_drop = [column for column in upper.columns if any(upper[column] > 0.8)]
final_features = [f for f in selected if f not in to_drop]
print(final_features)

This sequence ensures you keep only features that are both predictive and non-redundant.

Conclusion: When and Why to Choose PPS

Feature selection is a crucial step in building high-performing, interpretable machine learning models. While traditional methods like correlation are quick and intuitive, they fall short for modern, real-world datasets that include mixed data types and complex relationships.

The Predictive Power Score (PPS) is a robust, versatile, and interpretable alternative:

Detects both linear and non-linear relationships.
Handles numerical, categorical, and mixed data seamlessly.
Provides directionality, essential for predictive modeling.
Produces standardized, easy-to-interpret scores.

By integrating PPS into your feature selection workflow—potentially in combination with other filter and wrapper methods—you can discover hidden predictive patterns, boost your model’s accuracy, and improve interpretability.

Key Takeaways

Correlation is limited to linear, numerical relationships and is symmetric.
PPS measures predictive power for all data types, detects non-linear relationships, and is asymmetric.
PPS is easy to implement in Python and can be used early in the data exploration and modeling pipeline.
Always supplement PPS with checks for multicollinearity and domain knowledge for best results.

References and Further Reading

Final Thoughts

Feature selection is as much an art as a science. While tools like PPS provide powerful, automated insights, remember that the best features for your model are those that combine statistical significance, predictive power, and relevance to the business or scientific question at hand. Use PPS as a guide—but let your final choices be informed by the unique context of your data and problem.

If you want to go beyond correlation for feature selection, start using PPS today—and unlock the full predictive potential of your data!