title: Regularized Multitask Learning for Multidimensional Log-Density Gradient Estimation.
abstract: Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring nongaussianity. 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 letter is to improve the performance of this direct method in multidimensional cases. Our idea is to regard the problem of log-density gradient estimation in each dimension as a task and apply regularized multitask learning to the direct log-density gradient estimator. We experimentally demonstrate the usefulness of the proposed multitask method in log-density gradient estimation and mode-seeking clustering.
authors.affiliation: Graduate School of Frontier Sciences, University of Tokyo, Kashiwa-shi, Chiba 277-8561, Japan yamane@ms.k.u-tokyo.ac.jp.
authors.forename: Ikko
authors.initials: I
authors.lastname: Yamane
authors.affiliation: Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma-shi, Nara 630-0192, Japan hsasaki@naist.jp.
authors.forename: Hiroaki
authors.initials: H
authors.lastname: Sasaki
authors.affiliation: Graduate School of Frontier Sciences, University of Tokyo, Kashiwa-shi, Chiba 277-8561, Japan sugi@k.u-tokyo.ac.jp.
authors.forename: Masashi
authors.initials: M
authors.lastname: Sugiyama