Machine Learning with Squared-Loss Mutual Information

• Main Author: Masashi Sugiyama
• Format: Article
• Language: English
• Published: MDPI AG 2012-12-01
• Series: Entropy
• Subjects: squared-loss mutual information; Pearson divergence; density-ratio estimation; independence testing; dimensionality reduction; independent component analysis; object matching; clustering; causal inference; machine learning
• Online Access: http://www.mdpi.com/1099-4300/15/1/80

Mutual information (MI) is useful for detecting statistical independence between random variables, and it has been successfully applied to solving various machine learning problems. Recently, an alternative to MI called squared-loss MI (SMI) was introduced. While ordinary MI is the Kullback–Leibler divergence from the joint distribution to the product of the marginal distributions, SMI is its Pearson divergence variant. Because both the divergences belong to the ƒ-divergence family, they share similar theoretical properties. However, a notable advantage of SMI is that it can be approximated from data in a computationally more efficient and numerically more stable way than ordinary MI. In this article, we review recent development in SMI approximation based on direct density-ratio estimation and SMI-based machine learning techniques such as independence testing, dimensionality reduction, canonical dependency analysis, independent component analysis, object matching, clustering, and causal inference.