Conditional Density Estimation with Dimensionality Reduction via Squared-Loss Conditional Entropy Minimization

TL;DR

This paper introduces a unified method for conditional density estimation that simultaneously performs dimensionality reduction by minimizing a squared-loss variant of conditional entropy, improving accuracy in high-dimensional settings.

Contribution

The proposed approach integrates dimensionality reduction and conditional density estimation into a single process, avoiding error propagation from separate steps.

Findings

Effective in high-dimensional data scenarios

Outperforms traditional two-step methods

Validated on diverse datasets including robotics and art

Abstract

Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional density itself is preferable, but conditional density estimation (CDE) is challenging in high-dimensional space. A naive approach to coping with high-dimensionality is to first perform dimensionality reduction (DR) and then execute CDE. However, such a two-step process does not perform well in practice because the error incurred in the first DR step can be magnified in the second CDE step. In this paper, we propose a novel single-shot procedure that performs CDE and DR simultaneously in an integrated way. Our key idea is to formulate DR as the problem of minimizing a squared-loss variant of conditional entropy, and this is solved via CDE. Thus, an additional CDE step is not needed after DR. We demonstrate the usefulness of the proposed method through extensive experiments on various datasets including humanoid robot transition and computer art.