publication . Other literature type . Conference object . Preprint . 2016

Agnostic Estimation of Mean and Covariance

Lai, Kevin A.; Rao, Anup B.; Vempala, Santosh;
  • Published: 23 Apr 2016
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Abstract
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 inf...
Subjects
arXiv: Computer Science::Machine Learning
ACM Computing Classification System: MathematicsofComputing_NUMERICALANALYSIS
free text keywords: Robust statistics, Applied mathematics, Gaussian, symbols.namesake, symbols, Covariance, Discrete mathematics, Singular value decomposition, Corollary, Mean estimation, Computer science, Computer Science - Data Structures and Algorithms, Computer Science - Learning, Statistics - Machine Learning
Related Organizations

[AGMS12] Sanjeev Arora, Rong Ge, Ankur Moitra, and Sushant Sachdeva. Provable ICA with unknown gaussian noise, with implications for gaussian mixtures and autoencoders. In NIPS, pages 2384-2392, 2012.

Ricardo A. Maronna, Werner A. Stahel, and Victor J. Yohai. Bias-robust estimators of multivariate scatter based on projections. J. Multivar. Anal., 42(1):141-161, July 1992. [OpenAIRE]

Michael McCoy, Joel A Tropp, et al. Two proposals for robust pca using semidefinite programming. Electronic Journal of Statistics, 5:1123-1160, 2011.

Ankur Moitra and Gregory Valiant. Settling the polynomial learnability of mixtures of Gaussians. In Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on, pages 93-102. IEEE, 2010. [OpenAIRE]

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publication . Other literature type . Conference object . Preprint . 2016

Agnostic Estimation of Mean and Covariance

Lai, Kevin A.; Rao, Anup B.; Vempala, Santosh;