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Machine learning with squared-loss mutual information. (English) Zbl 1371.68241
Summary: 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 $$f$$-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.

##### MSC:
 68T05 Learning and adaptive systems in artificial intelligence 62B10 Statistical aspects of information-theoretic topics 62H25 Factor analysis and principal components; correspondence analysis 62H30 Classification and discrimination; cluster analysis (statistical aspects)
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