OCAMI Report
Online Seminar
Date : February 28 (Fri.) 2025, 16:30–18:00 JST
Style : Online by Zoom
Speaker : Bartosz Kołodziejek (Warsaw University of Technology)
Title : High-dimensional pattern recovery with general polyhedral norms
Abstract :
In my talk, I will consider the high-dimensional estimation of the concentration matrix (i.e., the inverse covariance matrix) and the recovery of its underlying pattern. Our approach is based on the penalized log-determinant Bregman divergence, which, under the Gaussian model, coincides with the penalized log-likelihood framework. The penalty is imposed via a norm applied to the off-diagonal elements of symmetric matrices. When this norm is polyhedral—meaning its unit ball is a polyhedron—a natural notion of pattern arises. Notably, when the $\ell_1$ norm is used, this notion of pattern corresponds to the signs of the off-diagonal elements of the concentration matrix, a setting that has been previously studied in [1]. Our work not only generalizes these results to arbitrary polyhedral norms but also substantially relaxes the sufficient conditions required for successful pattern recovery. This talk is based on joint work with Hideto Nakashima, Piotr Graczyk, and Maciej Wilczyński.
[1] Ravikumar, Pradeep; Wainwright, Martin J.; Raskutti, Garvesh; Yu, Bin. High-dimensional covariance estimation by minimizing $\ell_1$-penalized log-determinant divergence. Electron. J. Stat. 5 (2011), 935--980
Workshop
Date : December 4--5 2024
Place : Osaka Metropolitan University (I-siteなんば), 2-1-41, Shikitsuhigashi, Naniwa-ku, Osaka-shi, Osaka, Japan
Style : Hybrid (onsite and Zoom)
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:
https://forms.office.com/r/E8C1fb16pp
The Zoom information will be sent to you at a later date.
Speakers (alphabetical order)
Carlos Améndola (Technical University of Berlin)
Yuka Hashimoto (NTT)
Bruno Lourenço (The Institute of Statistical Mathematics)
Thomas Möllenhoff (RIKEN AIP)
Hiroyuki Sato (Ritsumeikan University)
Sho Sonoda (RIKEN AIP)
Ushio Tanaka (Osaka Metropolitan University)
Daisuke Tarama (Ritsumeikan University)
Takashi Tsuchiya (National Graduate institute for Policy Studies)
Program
December 4 (Wednesday)
13:00--13:50 Thomas Möllenhoff (RIKEN AIP)
Variational Learning is Effective for Large Deep Networks
14:00--14:50 Yuka Hashimoto (NTT / RIKEN AIP)
Reproducing kernel Hilbert $C^∗$-module for data analysis
15:00--15:50 Sho Sonoda (RIKEN AIP)
Deep Ridgelet Transform: Harmonic Analysis for Deep Learning Machine
16:10--17:00 Carlos Améndola (Technical University of Berlin)
Maximum likelihood estimation of log-affine models using reaction networks
December 5 (Thursday)
10:00--10:50 Bruno Lourenço (The Institute of Statistical Mathematics)
Facial structure of homogeneous convex cones
11:00--11:50 Ushio Tanaka (Osaka Metropolitan University), Tomonari Sei (The University of Tokyo)
Geometric analysis on a quantification
13:30--14:20 Daisuke Tarama (Ritsumeikan University)
Geodesic flows associated to statistical transformation models
14:30--14:55 Hikozo Kobayashi (Hiroshima University)
Moduli spaces of left-invariant statistical structures, dually-flatness and conjugate symmetries
14:55--15:20 Keiji Yahata (The University of Tokyo)
Duality for One-Dimensional Exponential Families
15:40--16:30 Hiroyuki Sato (Ritsumeikan University)
Optimization theory on manifolds and its applications
16:40--17:30 Takashi Tsuchiya (National Graduate Institute for Policy Studies)
Closing nonzero duality gaps of singular semidefinite programs by perturbation
Organizers
Hiroto Inoue (Nishinippon Institute of Technology)
Koichi Tojo (RIKEN AIP)
Hideto Nakashima (The Institute of Statistical Mathematics)
Yoshihiko Konno (Osaka Metropolitan University)
Piotr Graczyk (University of Angers)
Hideyuki Ishi (Osaka Metropolitan University)
Kenji Fukumizu (The Institute of Statistical Mathematics)
contact: hinoue[at]nishitech.ac.jp
Sponsor
This work was partly supported by MEXT Promotion of Distinctive Joint Research Center Program JPMXP0723833165.