Minimum Gamma-Divergence for Regression and Classification Problems

Shinto Eguchi received his master degree from Osaka University in 1979 and a Ph.D. from Hiroshima University, Japan, in 1984. His working career started as Assistant Professor of Hiroshima University, 1984, Associate Professor of Shinamne University, 1986, and Professor of The Institute of Statistical Mathematics, 1995-2020. He is currently Emeritus Professor at the Institute of Statistical Mathematics and Graduate University of Advanced Studies. His research interest is primarily statistics, including statistical machine learning, bioinformatics, information geometry, statistical ecology and parametric/semiparametric inference and robust statistics. His recent publication: -A generalized quasi-linear mixed-effects model, Y Saigusa, S Eguchi, O Komori, Statistical Methods in Medical Research, 31 (7), 1280-1291, 2022. -Robust self-tuning semiparametric PCA for contaminated elliptical distribution, H Hung, SY Huang, S Eguchi, IEEE Transactions on Signal Processing 70, 5885-5897, 2022. -Minimum information divergence of Q-functions for dynamic treatment resumes. S Eguchi, Information Geometry, 1-21, 2022.

• 1. Introduction.- 2. Framework of gamma-divergence.- 2.1. Scale invariance.- 2.2 GM divergence and HM divergence.- 3. Minimum divergence methods for generalized linear models.- 3.1. Bernoulli logistic model.- 3.2. Poisson log-linear model.- 3.3. Poisson point process model.- 4. Minimum divergence methods in machine leaning.- 4.1. Multi-class AdaBoost.- 4.2. Boltzmann machine.- 5. gamma-divergence for real valued functions.- 6. Discussion.