[Paper Review] Prediction Rule Reshaping

Matt Bonakdarpour, Sabyasachi Chatterjee+2 more|arXiv (Cornell University)|May 16, 2018

Fuzzy Logic and Control Systems3 citations

TL;DR

This paper proposes two methods for reshaping pre-trained prediction rules—black box reshaping and random forest-specific reshaping—to enforce monotonicity and convexity constraints in high-dimensional regression and classification. Both methods efficiently reconfigure predictions while preserving accuracy, demonstrating that shape constraints can be imposed without sacrificing predictive performance on four real-world datasets.

ABSTRACT

Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied to any pre-trained prediction rule, while the second method deals specifically with random forests. In both cases, efficient algorithms are developed for computing the estimators, and experiments are performed to demonstrate their performance on four datasets. We find that reshaping methods enforce shape constraints without compromising predictive accuracy.

Motivation & Objective

• To address the challenge of enforcing shape constraints like monotonicity and convexity in high-dimensional regression and classification tasks.
• To develop a flexible framework that applies to any pre-trained prediction rule, enabling shape constraints without retraining.
• To create a specialized method for reshaping random forests while preserving their predictive power and structural integrity.
• To demonstrate that shape-constrained predictions can maintain high accuracy, even in high-dimensional settings.
• To provide a practical, efficient solution for deploying interpretable models in real-world applications where monotonicity or convexity is scientifically or ethically required.

Proposed method

• Black box reshaping reformulates predictions by solving a constrained optimization problem to enforce monotonicity or convexity in specified variables, using an efficient isotonization algorithm.
• The method minimizes the L2 distance between the original prediction rule and the reshaped function that satisfies the shape constraints.
• For random forests, the reshaping operates on individual decision trees by adjusting leaf values while preserving split rules and tree structure.
• An efficient algorithm is developed for isotonization in multiple dimensions, enabling joint reshaping across predictors rather than one-dimensional sorting.
• The approach is model-agnostic, allowing application to any pre-trained model, including random forests, gradient boosted trees, or deep learning models.
• The framework supports both regression and classification tasks, with shape constraints applied to specific input variables as needed.

Experimental results

Research questions

• RQ1 Can shape constraints such as monotonicity and convexity be effectively enforced on high-dimensional prediction rules without degrading predictive accuracy?
• RQ2 How can a pre-trained model be reshaped to satisfy shape constraints while preserving its original predictive performance?
• RQ3 What is the computational efficiency of reshaping methods when applied to large-scale datasets with high-dimensional inputs?
• RQ4 Can reshaping be applied to complex models like random forests without altering their structural components?
• RQ5 How do reshaped predictions compare to original models in terms of accuracy and constraint enforcement across diverse real-world datasets?

Key findings

• The reshaping methods successfully enforce monotonicity and convexity constraints on all four datasets without compromising predictive accuracy.
• On the diabetes dataset, all estimators—including reshaped random forests—achieved nearly identical mean squared error, indicating no loss in accuracy.
• For the Zillow dataset, mean absolute percent error (MAPE) remained indistinguishable across all methods, even with large constraint sets.
• In the Adult dataset, test set accuracy was preserved after reshaping for income prediction, with monotonicity enforced on capital gain, weekly hours, education level, and gender wage gap.
• On the Spambase dataset, the probability of spam classification was monotonically decreasing with respect to 'george' and 'hp' word frequencies after reshaping, with no drop in performance.
• The methods are computationally efficient and scalable, with the black box approach applicable to any pre-trained model, and the random forest method preserving tree structure while enforcing constraints.