Agnostic Estimation of Mean and Covariance

Code

• github.com/kal2000/AgnosticMeanAndCovarianceCode
  OfficialIn papernone★ 14
• github.com/hoonose/robust-filter
  none★ 0

Abstract

We consider the problem of estimating the mean and covariance of a distribution from iid samples in R^n, in the presence of an 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 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.

Reproductions