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# Mean estimation in high dimensions

Speaker: Prayaag
Title: Mean estimation in high dimensions
Date: 15 Oct 2018 5:30pm-7:00pm
Location: Maxwell-Dworkin 123
Food: Unknown
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Abstract: Given samples from a multivariate Gaussian distribution, it is known that the empirical mean achieves the “best” possible confidence intervals around the true mean. Now, suppose that one is given samples from a multivariate distribution whose mean and covariance are finite, but is no longer promised to be Gaussian. In this setting, the empirical mean achieves very poor concentration around the true mean, compared with the Gaussian case. Can one design an estimator of the mean which achieves the same concentration around the true mean as in the Gaussian case? In 2017, Lugosi and Mendelson answered this question in the affirmative, but did not provide an efficient algorithm for computing their estimator. In 2018, Hopkins gave an algorithm for computing this estimator which runs in polynomial time. I will discuss this mean estimation problem, provide some intuition for the polynomial time estimator, and state some related open problems.

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