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• W3204142203 abstract "Abstract We study the statistical estimation problem of orthogonal group synchronization and rotation group synchronization. The model is $Y_{ij} = Z_i^* Z_j^{*T} + sigma W_{ij}in{mathbb{R}}^{dtimes d}$ 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 $(1+o(1))frac{sigma ^2 d(d-1)}{2np}$ when initialized by spectral methods. A matching minimax lower bound is further established that leads to the optimality of the proposed algorithm as it achieves the exact minimax risk." @default.
• W3204142203 created "2021-10-11" @default.
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• W3204142203 date "2022-08-06" @default.
• W3204142203 modified "2023-10-17" @default.
• W3204142203 title "Optimal orthogonal group synchronization and rotation group synchronization" @default.
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• W3204142203 doi "https://doi.org/10.1093/imaiai/iaac022" @default.
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