Direct Importance Estimation with Gaussian Mixture Models

Makoto YAMADA  Masashi SUGIYAMA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E92-D   No.10   pp.2159-2162
Publication Date: 2009/10/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E92.D.2159
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Pattern Recognition
Keyword: 
importance weight,  KLIEP,  Gaussian mixture models,  EM algorithm,  

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Summary: 
The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method--which we call the Gaussian mixture KLIEP (GM-KLIEP)--is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.