Regularized Multi-Task Learning for Multi-Dimensional Log-Density Gradient Estimation
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.
Cite
@article{arxiv.1508.00085,
title = {Regularized Multi-Task Learning for Multi-Dimensional Log-Density Gradient Estimation},
author = {Ikko Yamane and Hiroaki Sasaki and Masashi Sugiyama},
journal= {arXiv preprint arXiv:1508.00085},
year = {2015}
}