A Field-Theoretic View of Unlabeled Sensing
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909377254916096 |
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| author | Liang, Hao Lu, Jingyu Tsakiris, Manolis C. Zhi, Lihong |
| author_facet | Liang, Hao Lu, Jingyu Tsakiris, Manolis C. Zhi, Lihong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01175 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Field-Theoretic View of Unlabeled Sensing Liang, Hao Lu, Jingyu Tsakiris, Manolis C. Zhi, Lihong Commutative Algebra Information Theory Signal Processing 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. |
| title | A Field-Theoretic View of Unlabeled Sensing |
| topic | Commutative Algebra Information Theory Signal Processing |
| url | https://arxiv.org/abs/2303.01175 |