A Unified Framework of Density Ratio Estimation under Bregman Divergence

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概要

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• Estimation of the ratio of probability densities has attracted a great deal of attention since it can be used for addressing various statistical paradigms such as non-stationarity adaptation, two-sample test, outlier detection, mutual information estimation, dimensionality reduction, independent component analysis, causal inference, conditional density estimation, and probabilistic classification. A naive approach to density ratio approximation is to first estimates numerator and denominator densities separately and then take their ratio. However, this two-step approach does not perform well in practice, and methods for directly estimating the density ratio without going through density estimation have been explored, including methods based on moment matching, probabilistic classification, density matching, and density-ratio fitting. The contributions of this paper are three folds: First, we give a comprehensive review of existing density ratio estimation methods and discuss their pros and cons. The second contribution is that we propose a new framework of density ratio estimation in which a density-ratio model is fitted to the true density-ratio under the Bregman divergence. Our new framework includes all the above existing approaches as special cases, and is substantially more general. Thus, it provides a unified view of various density ratio estimation methods. Finally, we develop a robust density ratio estimation method under the power divergence, which is a novel instance in our framework.

• 2010-10-28

著者

• Sugiyama Masashi

  Tokyo Inst. Of Technol.

• KANAMORI Takafumi

  Nagoya University

• Suzuki Taiji

  University of Tokyo

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