Conformalized High-Density Quantile Regression via Dynamic Prototypes-based Probability Density Estimation
This work addresses scalability and accuracy issues in quantile regression for heteroscedastic, multimodal, or skewed data, though it appears incremental as an enhancement to existing regression-as-classification frameworks.
The paper tackles the limitations of existing quantile regression methods that use fixed quantization bins by introducing a conformalized approach with dynamically adaptive prototypes, achieving high-quality prediction regions with improved coverage and robustness while using fewer prototypes and memory.
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 .