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arXiv · 2303.01175

A Field-Theoretic View of Unlabeled Sensing

Hao Liang·Jingyu Lu·Manolis C. Tsakiris·Lihong Zhi
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Abstract

Unlabeled sensing is the problem of solving a linear system of equations, where the right-hand-side vector is known only up to a permutation. In this work, we study fields of rational functions related to symmetric polynomials and their images under a linear projection of the variables; as a consequence, we establish that the solution to an n-dimensional unlabeled sensing problem with generic data can be obtained as the unique solution to a system of n + 1 polynomial equations of degrees 1, 2, . . . , n + 1 in n unknowns. Besides the new theoretical insights, this development offers the potential for scaling up algebraic unlabeled sensing algorithms.

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BibTeXRIS

Hao Liang, Jingyu Lu, Manolis C. Tsakiris, Lihong Zhi. 2023-03-02. A Field-Theoretic View of Unlabeled Sensing. https://arxiv.org/abs/2303.01175

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