  We consider the problem of estimating the mean and covariance of a
distribution from iid samples in $\mathbb{R}^n$, in the presence of an $\eta$
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 $\eta$ 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.
