Direct importance estimation with probabilistic principal component analyzers

The importance estimation problem (estimating the ratio of two probability density functions) has recently gathered a great deal of attention for use in various applications, e.g., outlier detection and covariate shift adaptation. In this paper, we propose a new importance estimation method using mixtures of probabilistic principal component analyzers (PPCAs). Our method employs the framework of the Kullback-Leibler importance estimation procedure (KLIEP) using using linear or kernel models. The proposed approach entitled PPCA mixture KLIEP (PM-KLIEP) can improve importance estimation accuracy with correlated and rank-deficient data. Through experiments, we show the validity of the proposed approach.