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タイトル Projective limit combinatorial models for Number Place puzzle and self-avoiding walks on lattice.
開催日時 2019年5月23日 13:00 - 14:00 + 30 min
主催者
講演者 Masahiro Nakano氏
場所 Keio Univ. Yagami-campus Bldg.14th, 6F
Room 631A/B
内容 Bayesian nonparametric machine learning aims to make it possible to analyze infinitely many data via infinite-dimensional parametric models. One of the main topic of this area of research is how to find or construct essentially new stochastic processes. We first briefly review its history of over 20 years, and address some key notions in this field, including computability, exchangeability, projectivity, and conditional projectivity. Then we clarify some open issues for technical nuisances. For example, conditioning (i.e., parametric models) has been a key tool in Bayesian statistics, however, conditional probabilities are not always computable [arXiv:1005.3014]. This result implies that some additional assumptions are always required for the construction of parametric models. In this talk, as case studies, we deal with Number Place puzzle and self-avoiding walks on lattice, and tackle the constructions of infinite-dimensional parametric models whose supports are all possible patterns of them with infinite size.
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