2021/09/28 by Chao Gao, Gao, Chao, Anderson Y. Zhang +1
Chemistry · Computer Science · Physics and Astronomy · #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Molecular spectroscopy and chirality #Optimization and Control (math.OC) #Quantum optics and atomic interactions #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2109.13491
openalex publication_date 2021/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the statistical estimation problem of orthogonal group synchronization and rotation group synchronization. The model is Yij = Zi^* Zj*T + σWij∈ℝd× d where Wij is a Gaussian random matrix and Zi^* is either an orthogonal matrix or a rotation matrix, and each Yij 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))(σ2 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.