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.

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