Problem Description

You are tasked with designing an end-to-end regression pipeline to predict the 90-day customer lifetime value (CLV_90) at the individual user level.

Context

The target variable, CLV_90, exhibits specific characteristics:

• Many zero values (zero-inflation).
• A heavy right tail (skewed distribution).

Features are available up to a fixed cutoff date for each user and include:

• Continuous Spend Features: Spend_SEM, Spend_Social, Spend_Display.
• RFM Features: Recency, Frequency, Monetary.
• Categorical Features: Device, Region, Tenure.
• High-Cardinality Features: Dozens of sparse campaign IDs.

Known challenges with the dataset include:

• Strong multicollinearity among the continuous spend channels.
• Heteroskedastic errors.
• Nonlinear effects within the data.

Task Requirements

Your design must address the following aspects:

1. Loss Function and Distribution: Select and justify an appropriate loss function and underlying distribution for the target variable. Consider options such as log-link Generalized Linear Models (GLM), Tweedie distribution, zero-inflated or hurdle models, quantile regression, or gradient-boosted regression.
2. Feature Processing: Detail the necessary feature engineering steps, including:
   • log1p transformations.
   • Standardization.
   • Bucketing of rare categories.
   • Target encoding for high-cardinality features, specifically using K-fold out-of-fold encoding to prevent data leakage.
3. Multicollinearity and Feature Selection: Propose methods to handle multicollinearity and perform feature selection. This should include a discussion of Ridge, Lasso, and Elastic Net regularization. You must write the objective function for Elastic Net, clearly defining the roles of its α and λ parameters and explaining when each penalty type (L1 vs. L2) dominates.
4. Cross-Validation Strategy: Design a time-based nested cross-validation scheme. Explain how this strategy prevents leakage from future signals and avoids issues related to campaign overlap.
5. Model Assumption Diagnosis and Mitigation: Describe how to diagnose and mitigate common model assumption violations:
   • Heteroskedasticity: Discuss robust standard errors, variance-stabilizing transformations, or leveraging the mean-variance relationship in Tweedie models.
   • Nonlinearity: Address with techniques like splines or interaction terms.
   • Influential Outliers: Mitigate using robust loss functions such as Huber or Tukey loss.
6. Prediction Intervals: Provide a method for generating calibrated 95% prediction intervals for CLV_90. Compare approaches like conformal prediction or bootstrapping against traditional Ordinary Least Squares (OLS) analytic intervals.
7. Effect Interpretation: Explain how to interpret feature effects. Compare standardized coefficients from a regularized linear model with SHAP (SHapley Additive exPlanations) values from a tree-based model.
8. Data Leakage Risks: Identify, quantify, and propose mitigations for data leakage risks. Specifically address target leakage from post-cutoff features and look-ahead bias in target encoding.
9. Model Comparison and Metrics: Compare the performance and interpretability trade-offs between a regularized linear model and a gradient-boosting model. Specify evaluation metrics that are robust to heavy-tailed distributions, such as Mean Absolute Error (MAE), Quantile loss, or Mean Absolute Percentage Error (MAPE) with an epsilon term.