Convex Regression with Interpretable Sharp Partitions.

Area of Science:

• Statistics
• Machine Learning
• Predictive Modeling

Background:

• Predicting outcomes with interpretable models is crucial.
• Non-additive relationships often present challenges for standard regression techniques.
• Existing partitioning methods may suffer from high variance or greedy approaches.

Purpose of the Study:

• To propose a novel interpretable and non-additive modeling approach for outcome prediction.
• To introduce Convex Regression with Interpretable Sharp Partitions (CRISP).
• To evaluate the performance and properties of CRISP.

Main Methods:

• CRISP partitions the covariate space into data-adaptive blocks.
• A mean model is fitted within each block.
• The model is solved using a non-greedy convex optimization approach, ensuring low-variance fits.

Main Results:

• CRISP provides interpretable partitions of the covariate space.
• The convex optimization approach leads to stable and low-variance predictions.
• Evaluations through simulation and a housing price dataset demonstrate CRISP's effectiveness.

Conclusions:

• CRISP offers a powerful and interpretable method for non-additive regression.
• The approach balances interpretability with predictive accuracy.
• CRISP is a promising alternative for outcome prediction tasks with complex covariate relationships.