Regularized Multi-Task Learning for Multi-Dimensional Log-Density Gradient Estimation

TL;DR

This paper introduces a regularized multi-task learning approach to improve multi-dimensional log-density gradient estimation, which is crucial for clustering and non-Gaussianity measurement, outperforming traditional two-step methods.

Contribution

It proposes a novel multi-task learning framework for direct log-density gradient estimation in multiple dimensions, enhancing accuracy over existing methods.

Findings

Multi-task learning improves gradient estimation accuracy.

Enhanced mode-seeking clustering performance.

Method outperforms two-step density estimation approaches.

Abstract

Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring non-Gaussianity. A naive two-step approach of first estimating the density and then taking its log-gradient is unreliable because an accurate density estimate does not necessarily lead to an accurate log-density gradient estimate. To cope with this problem, a method to directly estimate the log-density gradient without density estimation has been explored, and demonstrated to work much better than the two-step method. The objective of this paper is to further improve the performance of this direct method in multi-dimensional cases. Our idea is to regard the problem of log-density gradient estimation in each dimension as a task, and apply regularized multi-task learning to the direct log-density gradient estimator. We experimentally demonstrate the usefulness of the proposed multi-task method in log-density gradient estimation and mode-seeking clustering.