We study the statistical estimation problem of orthogonal group synchronization and rotation group synchronization. The model is $Y_{ij} = Z_i^* Z_j^{*T} + \sigma W_{ij}\in{\mathbb{R}}^{d\times d}$ 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.
This content will become publicly available on August 9, 2024
Synchronization Storage Channels (S2C): Timer-less Cache Side-Channel Attacks on the Apple M1 via Hardware Synchronization Instructions
- Award ID(s):
- 1816282
- NSF-PAR ID:
- 10477383
- Publisher / Repository:
- USENIX
- Date Published:
- Journal Name:
- 32nd USENIX Security Symposium
- Format(s):
- Medium: X
- Location:
- Anaheim, CA, USA
- Sponsoring Org:
- National Science Foundation
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