Direct density-ratio estimation with dimensionality reduction via least-squares hetero-distributional subspace search.

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, D(3)-LHSS (Direct Density-ratio estimation with Dimensionality reduction via Least-squares Hetero-distributional Subspace Search), is shown to overcome the limitation of baseline methods.