Estimating Squared-Loss Mutual Information for Independent Component Analysis

Accurately evaluating statistical independence among random variables is a key component of Independent Component Analysis (ICA). In this paper, we employ a squared-loss variant of mutual information as an independence measure and give its estimation method. Our basic idea is to estimate the ratio of probability densities directly without going through density estimation, by which a hard task of density estimation can be avoided. In this density-ratio approach, a natural cross-validation procedure is available for model selection. Thanks to this, all tuning parameters such as the kernel width or the regularization parameter can be objectively optimized. This is a highly useful property in unsupervised learning problems such as ICA. Based on this novel independence measure, we develop a new ICA algorithm named Least-squares Independent Component Analysis (LICA).