Regularized Multitask Learning for Multidimensional Log-Density Gradient Estimation
Regularized Multitask Learning for Multidimensional Log-Density Gradient Estimation
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DOI：
10.1162/neco_a_00844
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发表时间：
2014-11
影响因子：
2.9
通讯作者：
Ikko Yamane;Hiroaki Sasaki;Masashi Sugiyama
中科院分区：
文献类型：
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作者：
Ikko Yamane;Hiroaki Sasaki;Masashi Sugiyama
对数密度梯度估计是一个基本的统计问题，在聚类和非高斯性度量等方面有着广泛的应用。首先估计密度然后取其对数梯度的简单两步方法是不可靠的，因为准确的密度估计不一定导致准确的对数密度梯度估计。为了科普这个问题，一种方法来直接估计对数密度梯度没有密度估计已被探索和证明工作得比两步方法。这封信的目的是提高这种直接方法在多维情况下的性能。我们的想法是把每个维度上的对数密度梯度估计问题作为一个任务，并将正则化多任务学习应用于直接对数密度梯度估计器。我们的实验表明，所提出的多任务方法在对数密度梯度估计和模式寻求聚类的有用性。
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.