: Sugiyama, M.; Yamada, M.; Bünau, P. von; Suzuki, T.; Kanamori, T.; Kawanabe, M.

Abstract
Methods for directly estimating the ratio of two probability density functions have been actively explored recently since they can be used for various data processing tasks such as non-stationarity adaptation, outlier detection, and feature selection. In this paper, we develop a new method which incorporates dimensionality reduction into a direct density-ratio estimation procedure. Our key idea is to find a low-dimensional subspace in which densities are significantly different and perform density-ratio estimation only in this subspace. The proposed method, D3-LHSS (Direct Density-ratio estimation with Dimensionality reduction via Least-squares Hetero-distributional Subspace Search), is shown to overcome the limitation of baseline methods.