Papers › Agnostic Estimation of Mean and Covariance
Agnostic Estimation of Mean and Covariance
Kevin A. Lai, Anup B. Rao, Santosh Vempala
We consider the problem of estimating the mean and covariance of a distribution from iid samples in ℝⁿ, in the presence of an η fraction of malicious noise; this is in contrast to much recent work where the noise itself is assumed to be from a distribution of known type. The agnostic problem includes many interesting special cases, e.g., learning the parameters of a single Gaussian (or finding the best-fit Gaussian) when η fraction of data is adversarially corrupted, agnostically learning a mixture of Gaussians, agnostic ICA, etc. We present polynomial-time algorithms to estimate the mean and covariance with error guarantees in terms of information-theoretic lower bounds. As a corollary, we also obtain an agnostic algorithm for Singular Value Decomposition.
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