Easy, robust approximate message passing for planted spike models
We present a simple and efficient algorithm for robust approximate message passing (AMP) in the spiked matrix setting. In particular, let $\varepsilon$ be a sufficiently small constant, and suppose that $X \in \mathbb R^{n \times n}$ is a Gaussian matrix with a planted rank-$1$ spike, and $E \in \mathbb R^{n \times n}$ is an adversarially chosen matrix supported on an $\varepsilon n \times \varepsilon n$ principal minor. Let $v_{\mathrm{AMP}}(X)$ be the output of an AMP iteration on the uncorrupted matrix $X$. We give a procedure that, given access only to the corrupted matrix $Y = X + E$, computes a vector $v_{\mathrm{ALG}}(Y)$ which is $\tilde{O}(\sqrt{\varepsilon})$-close to $v_{\mathr...
| Authors | Misha Ivkov, Tselil Schramm |
|---|---|
| Primary category | cs.DS |
| Published | 30 May 2026 |
| Last updated at source | 30 May 2026 |
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