Fast, robust approximate message passing
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910685535928320 |
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| author | Ivkov, Misha Schramm, Tselil |
| author_facet | Ivkov, Misha Schramm, Tselil |
| contents | We give a fast, spectral procedure for implementing approximate-message passing (AMP) algorithms robustly. For any quadratic optimization problem over symmetric matrices $X$ with independent subgaussian entries, and any separable AMP algorithm $\mathcal A$, our algorithm performs a spectral pre-processing step and then mildly modifies the iterates of $\mathcal A$. If given the perturbed input $X + E \in \mathbb R^{n \times n}$ for any $E$ supported on a $\varepsilon n \times \varepsilon n$ principal minor, our algorithm outputs a solution $\hat v$ which is guaranteed to be close to the output of $\mathcal A$ on the uncorrupted $X$, with $\|\mathcal A(X) - \hat v\|_2 \le f(\varepsilon) \|\mathcal A(X)\|_2$ where $f(\varepsilon) \to 0$ as $\varepsilon \to 0$ depending only on $\varepsilon$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast, robust approximate message passing Ivkov, Misha Schramm, Tselil Data Structures and Algorithms Machine Learning We give a fast, spectral procedure for implementing approximate-message passing (AMP) algorithms robustly. For any quadratic optimization problem over symmetric matrices $X$ with independent subgaussian entries, and any separable AMP algorithm $\mathcal A$, our algorithm performs a spectral pre-processing step and then mildly modifies the iterates of $\mathcal A$. If given the perturbed input $X + E \in \mathbb R^{n \times n}$ for any $E$ supported on a $\varepsilon n \times \varepsilon n$ principal minor, our algorithm outputs a solution $\hat v$ which is guaranteed to be close to the output of $\mathcal A$ on the uncorrupted $X$, with $\|\mathcal A(X) - \hat v\|_2 \le f(\varepsilon) \|\mathcal A(X)\|_2$ where $f(\varepsilon) \to 0$ as $\varepsilon \to 0$ depending only on $\varepsilon$. |
| title | Fast, robust approximate message passing |
| topic | Data Structures and Algorithms Machine Learning |
| url | https://arxiv.org/abs/2411.02764 |