Optimal Orthogonal Group Synchronization and Rotation Group Synchronization

09/28/2021
by   Chao Gao, et al.
0

We study the statistical estimation problem of orthogonal group synchronization and rotation group synchronization. The model is Y_ij = Z_i^* Z_j^*T + σ W_ij∈ℝ^d× d where W_ij is a Gaussian random matrix and Z_i^* is either an orthogonal matrix or a rotation matrix, and each Y_ij is observed independently with probability p. We analyze an iterative polar decomposition algorithm for the estimation of Z^* and show it has an error of (1+o(1))σ^2 d(d-1)/2np when initialized by spectral methods. A matching minimax lower bound is further established which leads to the optimality of the proposed algorithm as it achieves the exact minimax risk.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/12/2022

Exact Minimax Optimality of Spectral Methods in Phase Synchronization and Orthogonal Group Synchronization

We study the performance of the spectral method for the phase synchroniz...
research
10/09/2020

Exact Minimax Estimation for Phase Synchronization

We study the phase synchronization problem with measurements Y=z^*z^*H+σ...
research
01/07/2021

SDP Achieves Exact Minimax Optimality in Phase Synchronization

We study the phase synchronization problem with noisy measurements Y=z^*...
research
05/09/2023

Rotation Synchronization via Deep Matrix Factorization

In this paper we address the rotation synchronization problem, where the...
research
06/17/2022

Robust Group Synchronization via Quadratic Programming

We propose a novel quadratic programming formulation for estimating the ...
research
05/30/2021

Parallelized Computation and Backpropagation Under Angle-Parametrized Orthogonal Matrices

We present a methodology for parallel acceleration of learning in the pr...
research
09/16/2020

A Unified Approach to Synchronization Problems over Subgroups of the Orthogonal Group

Given a group 𝒢, the problem of synchronization over the group 𝒢 is a co...

Please sign up or login with your details

Forgot password? Click here to reset