Statistical Theories and Machine Learning Using Geometric Methods
Date: December 14--15, 2023
Venue: Academic Extension Center (Osaka Metropolitan University) https://www.omu.ac.jp/bunkakouryu-center/english/
Contents: Workshop (Hybrid: physical/virtual) This workshop is held as a part of OCAMI Joint Usage/Research
Program and Abstract: PDF
Ragistration
To participate in this workshop, please make a registration from the following form:
The Zoom information will be sent to you at a later date.
Speakers (alphabetical order)
Adam Chojecki (Warsaw University of Technology), Hideyuki Ishi (Osaka Metropolitan University)
Hajime Fujita (Japan Women's University)
Hiroto Inoue (Nishinippon Institute of Technology)
Eren Mehmet Kiral (Keio University)
Satoshi Kuriki (The Institute of Statistical Mathematics)
Atsumi Ohara (University of Fukui)
Tomonari Sei (The University of Tokyo)
Eiki Shimizu (SOKENDAI)
Tomasz Skalski (Wroclaw University of Science and Technology)
Ushio Tanaka (Osaka Metropolitan University)
Hikaru Watanabe (The University of Tokyo)
Program
December 14 (Thursday):
13:00--13:50 Hiroto Inoue (Nishinippon Institute of Technology)
Mean-variance joint statistic valued in a real Siegel domain
14:00--14:50 Eren Mehmet Kiral (Keio University)
Bayesian Learning with Lie Groups
15:00--15:50 Hajime Fujita (Japan Women's University)
The generalized Pythagorean theorem on the compactifications of certain dually flat spaces via toric geometry
16:10--17:00 Atsumi Ohara (University of Fukui)
Doubly autoparallel structure and curvature integrals: An application to iteration complexity analysis of convex optimization
17:10--18:00 Adam Chojecki (Warsaw University of Technology), Hideyuki Ishi (Osaka Metropolitan University),
Uncovering Data Symmetries: Estimating Covariance Matrix in High-Dimensional Setting With ’gips’ R Package
18:10--19:00 Tomasz Skalski (Wroclaw University of Science and Technology)
Maximum likelihood estimation for discrete exponential families, its geometry and combinatorics
December 15 (Friday):
10:00--10:50 Tomonari Sei (The University of Tokyo)
Some open problems on minimum information dependence models
11:00--11:50 Tomonari Sei (The University of Tokyo), Ushio Tanaka (Osaka Metropolitan University)
Stein identity, Poincare inequality and exponential integrability on a metric measure space
13:50--14:40 Hikaru Watanabe (The University of Tokyo)
Infinite dimensional parameterized measure models
14:50--15:40 Eiki Shimizu (SOKENDAI)
Neural-Kernel Conditional Mean Embeddings
15:50--16:40 Satoshi Kuriki (The Institute of Statistical Mathematics)
Bonferroni method and tube method for heavy-tailed distributions
Satellite seminar
Date: January 25, 14:00--15:00
Venue: Osaka Metropolitan University, Sugimoto campus, Graduate School of Science/School of Science, E408, and Zoom
Speaker: Howard Barnum (University of New Mexico)
Title: Homogeneous cones with pure transitivity are symmetric cones
Abstract:
In the ``General Probabilistic Theories" framework, we model abstractly possible physical systems using a compact convex set of normalized states, with measurement probabilities given by affine functionals evaluated on states. The normalized states are the base of a cone of unnormalized states. The finite-dimensional quantum systems, and their narrow generalizations the Euclidean Jordan algebraic systems, have state cones that are homogeneous, but also self-dual, hence symmetric. Here, we show that a homogeneous cone has the additional property of ``pure transitivity", namely that the affine automorphism group of a base (``reversible transformations on normalized states")
acts transitively on the extreme points of that base (``pure states") if and only if it is a direct sum of isomorphic symmetric cones. I'll briefly discuss the physical and information-processing significance of these assumptions. I'll also describe additional assumptions that ensure that the system is a standard quantum system, i.e. that the cone is the positive semidefinite Hermitian complex matrices. If time permits I will also present unpublished results with C. Ududec, establishing, for general, not necessarily symmetric, homogeneous cones, that certain faces of the cone are projectivein the sense of Alfsen and Shultz, a notion closely related to the ``projection postulate" of quantum theory.
Co-authors: Cozmin Ududec, John van de Wetering (University of Amsterdam)
Organizers:
Koichi Tojo (RIKEN AIP)
Hideto Nakashima (The Institute of Statistical Mathematics)
Yoshihiko Konno (Osaka Metropolitan University)
Hideyuki Ishi (Osaka Metropolitan University)
Kenji Fukumizu (The Institute of Statistical Mathematics)
contact: koichi.tojo [at] riken.jp
Sponsor
This workshop is supported by the following institution and grant:
Osaka Central Advanced Mathematical Institute (MEXT Promotion of Distinctive Joint Research Center Program JPMXP0723833165), Osaka Metropolitan University.
Last modified: Dec. 3, 2023