カーネル密度比推定の統計的解析(学習問題の解析,テキスト・Webマイニング,一般)

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概要

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• The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), feature selection (mutual information), and conditional probability estimation. Several methods of directly estimating the density ratio have been recently developed, e.g., moment matching estimation, maximum-likelihood density-ratio estimation, and least-squares density-ratio fitting. In this paper, we propose a kernelized variant of the least-squares method for density-ratio estimation, which is called kernel unconstraint least-squares importance fitting (KuLSIF). We then investigate its fundamental statistical properties including a non-parametric convergence rate, an analytic-form solution and a leave-one-out cross-validation score. We further study its relation to other kernel-based density-ratio estimators. In experiments, we numerically compare various kernel-based density-ratio estimation methods, and show that KuLSIF compares favorably with other approaches.

• 2011-03-21

著者

• Sugiyama Masashi

  Tokyo Inst. Of Technol.

• KANAMORI Takafumi

  Nagoya University

• Suzuki Taiji

  University of Tokyo

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