### Web: http://arxiv.org/abs/2206.10942

June 23, 2022, 1:12 a.m. | Misha Ivkov, Pravesh K. Kothari

We give the first polynomial time algorithm for \emph{list-decodable
covariance estimation}. For any $\alpha > 0$, our algorithm takes input a
sample $Y \subseteq \mathbb{R}^d$ of size $n\geq d^{\mathsf{poly}(1/\alpha)}$
obtained by adversarially corrupting an $(1-\alpha)n$ points in an i.i.d.
sample $X$ of size $n$ from the Gaussian distribution with unknown mean $\mu_*$
and covariance $\Sigma_*$. In $n^{\mathsf{poly}(1/\alpha)}$ time, it outputs a
constant-size list of $k = k(\alpha)= (1/\alpha)^{\mathsf{poly}(1/\alpha)}$
candidate parameters that, with high probability, contains a
$(\hat{\mu},\hat{\Sigma})$ such that the …

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