Density Ratio Estimation: A Comprehensive Review

Density ratio estimation has attracted a great deal of attention in the statistics and machine learning communities since it can be used for solving various statistical data processing tasks such as non-stationarity adaptation, two-sample test, outlier detection, independence test, feature selection/extraction, independent component analysis, causal inference, and conditional probability estimation. When estimating the density ratio, it is preferable to avoid estimating densities since density estimation is known to be a hard problem. In this paper, we give a comprehensive review of density ratio estimation methods based on moment matching, probabilistic classification, and ratio matching.