2012/12/12 by Francis Bach, Michael I. Jordan, Bach, Francis R. +1
Chemistry · Computer Science · #Blind Source Separation Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.1301.0554
openalex publication_date 2012/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a tree-structured graphical model. Treating the problem as a semiparametric statistical problem, we show that the optimal transform is found by minimizing a contrast function based on mutual information, a function that directly extends the contrast function used for classical ICA. We provide two approximations of this contrast function, one using kernel density estimation, and another using kernel generalized variance. This tree-dependent component analysis framework leads naturally to an efficient general multivariate density estimation technique where only bivariate density estimation needs to be performed.