Regularized multi-task learning for multi-dimensional log-density gradient estimation (情報論的学習理論と機械学習 情報論的学習理論ワークショップ) Regularized multi-task learning for multi-dimensional log-density gradient estimation

Log-density gradient estimation is a fundamental statistical problem and it has various practical applications such as clustering and a measure for non-Gaussianity. A naive two-step approach of first estimating the density and then taking its log-gradient does not perform well 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 was explored. However, even with the direct estimator, high-dimensional log-density gradient estimation is still challenging. In this paper, we propose to apply regularized multi-task learning to direct log-density gradient estimation and show its usefulness experimentally.