288 pp. per issue
6 x 9, illustrated
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Neural Computation

July 2016, Vol. 28, No. 7, Pages 1388-1410
(doi: 10.1162/NECO_a_00844)
© 2016 Massachusetts Institute of Technology
Regularized Multitask Learning for Multidimensional Log-Density Gradient Estimation
Article PDF (1017.44 KB)

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.