Identification of Matrix Joint Block Diagonalization
Apr 14, 2021
Speakers
Yunfeng Cai
Speaker · 0 followers
About
Given a set $\mathcal{C}=\{C_i\}_{i=1}^m$ of square matrices, the matrix blind joint block diagonalization problem (\bjbdp) is to find a full column rank matrix $A$ such that $C_i=A\Sigma_iA^{\T}$ for all $i$, where $\Sigma_i$'s are all block diagonal matrices with as many diagonal blocks as possible. The \bjbdp\ plays an important role in independent subspace analysis. This paper considers the identification problem for \bjbdp, that is, under what conditions and by what means, we can identify the diagonalizer $A$ and the block diagonal structure of $\Sigma_i$, especially when there is noise in $C_i$'s. In this paper, we propose a ``bi-block diagonalization'' method to solve \bjbdp, and establish sufficient conditions for when the method is able to accomplish the task. Numerical simulations validate our theoretical results. To the best of the authors' knowledge, current numerical methods for BJBDP have no theoretical guarantees for the identification of the exact solution, whereas our method does.Given a set $\mathcal{C}=\{C_i\}_{i=1}^m$ of square matrices, the matrix blind joint block diagonalization problem (\bjbdp) is to find a full column rank matrix $A$ such that $C_i=A\Sigma_iA^{\T}$ for all $i$, where $\Sigma_i$'s are all block diagonal matrices with as many diagonal blocks as possible. The \bjbdp\ plays an important role in independent subspace analysis. This paper considers the identification problem for \bjbdp, that is, under what conditions and by what means, we can identify t…
Organizer
AISTATS 2021
Account · 63 followers
Categories
AI & Data Science
Category · 10.8k presentations
About AISTATS 2021
The 24th International Conference on Artificial Intelligence and Statistics was held virtually from Tuesday, 13 April 2021 to Thursday, 15 April 2021.
Like the format? Trust SlidesLive to capture your next event!
Professional recording and live streaming, delivered globally.
Sharing
Recommended Videos
Presentations on similar topic, category or speaker
Asymptotics of Ridge(less) Regression under General Source Condition
Watch later
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Bandit algorithms: Letting go of logarithmic regret for statistical robustness
Watch later
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Generalization Bounds for Stochastic Saddle Point Problems
Watch later
Junyu Zhang, …
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Product Manifold Learning
Watch later
Sharon Zhang, …
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Provably Safe PAC-MDP Exploration Using Analogies
Watch later
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Oral: Neural Enhanced Belief Propagation on Factor Graphs
Watch later
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%