Talker: Daniel P. Palomar (HKUST)
(Joint work with Ying Sun and Prabhu Babu)
Title: Robust estimation of mean and covariance matrix for
heavy-tail distributions and outliers
Abstract: Consider the estimation problem of the mean and covariance
matrix for multi-dimensional samples drawn from a heavy-tailed
distribution. The traditional sample mean estimator and the sample
covariance matrix are extremely sensitive to heavy tails and
outliers and may completely fail. Indeed, if one naively assumes a
Gaussian distribution and proceeds, the final result may be
disastrous. We will focus on robust M-estimators for heavy-tailed
distributions, specifically the Cauchy MLE.
In addition, in practical settings the number of
samples may not be sufficient compared with the dimension of the
samples. We then consider regularization techniques that shrink the
estimators towards some prior information.
We establish the conditions for the existence and
uniqueness of the regularized estimator for finite samples and also
provide very efficient and practical algorithms with provable
convergence.
- slides
- video