Conformalized High-Density Quantile Regression via Dynamic Prototypes-based Probability Density Estimation

TL;DR

This paper introduces a conformalized high-density quantile regression method that adaptively optimizes prototypes for better prediction regions, offering improved coverage, robustness, and scalability in complex data scenarios.

Contribution

It proposes a novel dynamic prototypes-based approach with conformal guarantees, addressing quantization errors and high-dimensional challenges in quantile regression.

Findings

Achieves high-quality prediction regions with better coverage.

Uses fewer prototypes, reducing memory and computational costs.

Demonstrates robustness across diverse datasets and dimensions.

Abstract

Recent methods in quantile regression have adopted a classification perspective to handle challenges posed by heteroscedastic, multimodal, or skewed data by quantizing outputs into fixed bins. Although these regression-as-classification frameworks can capture high-density prediction regions and bypass convex quantile constraints, they are restricted by quantization errors and the curse of dimensionality due to a constant number of bins per dimension. To address these limitations, we introduce a conformalized high-density quantile regression approach with a dynamically adaptive set of prototypes. Our method optimizes the set of prototypes by adaptively adding, deleting, and relocating quantization bins throughout the training process. Moreover, our conformal scheme provides valid coverage guarantees, focusing on regions with the highest probability density. Experiments across diverse datasets and dimensionalities confirm that our method consistently achieves high-quality prediction regions with enhanced coverage and robustness, all while utilizing fewer prototypes and memory, ensuring scalability to higher dimensions. The code is available at https://github.com/batuceng/max_quantile .