Least-Squares Independence Test

Masashi SUGIYAMA  Taiji SUZUKI  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E94-D   No.6   pp.1333-1336
Publication Date: 2011/06/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E94.D.1333
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Artificial Intelligence, Data Mining
Keyword: 
independence test,  density ratio estimation,  unconstrained least-squares importance fitting,  squared-loss mutual information,  

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Summary: 
Identifying the statistical independence of random variables is one of the important tasks in statistical data analysis. In this paper, we propose a novel non-parametric independence test based on a least-squares density ratio estimator. Our method, called least-squares independence test (LSIT), is distribution-free, and thus it is more flexible than parametric approaches. Furthermore, it is equipped with a model selection procedure based on cross-validation. This is a significant advantage over existing non-parametric approaches which often require manual parameter tuning. The usefulness of the proposed method is shown through numerical experiments.