Algebraically-initialized Expectation Maximization for Header-free Communication

Abstract

Towards low-latency communication for short-packet transmission, this paper tackles the problem of shuffled linear regression for large-scale wireless sensor networks with header-free communication by using results from algebraic geometry as well as an alternating optimization scheme. The shuffled linear regression problem is to solve a linear system with shuffled entries of the right hand side vector. However, solving the shuffled linear system requires high computational cost. The key idea of our approach is to eliminate the shuffled structure via symmetric polynomials, which leads to a system of polynomial equations. Considering one of the solutions of the resulting polynomial system as an initialization to the Expectation Maximization algorithm, we propose the Algebraically-Initialized Expectation Maximization algorithm. Computational experiments with synthetic data show that our proposed algorithm is extensively efficient, and it performs well even with noise.