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math.ST2022
Recent Advances in Algebraic Geometry and Bayesian Statistics
Sumio Watanabe
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning m…
cs.LG2022
Mathematical Theory of Bayesian Statistics for Unknown Information Source
Sumio Watanabe
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware t…
cs.LG2022
Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures
Takumi Watanabe, Sumio Watanabe
Multinomial mixtures are widely used in the information engineering field, however, their mathematical properties are not yet clarified because they are singular learning models. I…