3-14-1 Kouhoku-ku, Hiyoshi, Yokohama 223-8522, JAPAN
speaker: Masahiro Nakano
title: Projective limit combinatorial models for Number Place puzzle and
self-avoiding walks on lattice.
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.
time: 13:00 - 14:00 + 30 min
place: Keio Univ. Yagami-campus Bldg.14th, 6F
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