2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) (2016)

New Brunswick, New Jersey, USA

Oct. 9, 2016 to Oct. 11, 2016

ISSN: 0272-5428

ISBN: 978-1-5090-3933-3

pp: 665-674

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2016.76

ABSTRACT

We consider the problem of estimating the mean and covariance of a distribution from i.i.d. samples in the presence of a 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 a fraction of data is adversarially corrupted, agnostically learning mixtures, 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.

INDEX TERMS

Estimation, Robustness, Complexity theory, Data models, Noise measurement, Principal component analysis, Computer science

CITATION

Kevin A. Lai,
Anup B. Rao,
Santosh Vempala,
"Agnostic Estimation of Mean and Covariance",

*2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)*, vol. 00, no. , pp. 665-674, 2016, doi:10.1109/FOCS.2016.76CITATIONS