[Theory] 11/14 TTIC Colloquium: Paul Valiant, Purdue University

[Mary Marre]

*When:*        Monday, November 14th at* 11:30 am CT*

*Where:     * Talk will be *live, in-person* at
                   TTIC, 6045 S. Kenwood Avenue

                   5th Floor, Room 530


*Virtually:*   Via Panopto (*livestream
<https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=a6540580-fb4e-4402-b1a9-af460182dc1f>*
)


*Who: *         Paul Valiant, Purdue University


------------------------------

*Title:*          Mean Estimation in Low and High Dimensions
*Abstract: *This talk will discuss the fundamental statistical problem of
estimating the mean of a distribution, as accurately as possible given
samples from it. This problem arises both as a subcomponent of many
algorithms, and also in practice as one of the most important data
primitives when dealing with real-world data. While many variants and
extensions of this problem have been proposed and analyzed, in this talk I
will discuss two of the most iconic: 1) when the data comes from a
real-valued distribution, and 2) when the data comes from a
high-dimensional vector-valued distribution. In both cases, we achieve the
first estimators whose accuracy is optimal to 1+o(1) factors, optimal in
its dependence on the unknown (co-) variance of the underlying
distribution, the number of samples n, and the desired confidence delta. I
will highlight some of the crucial and novel analytical tools used in the
analysis, and in particular, draw attention to a new "vector Bernstein
inequality" which makes precise the intuition that sums of bounded
independent random variables in increasingly high dimensions increasingly
"adhere to a spherical shell". These results suggest several possible
extensions in this large and active area of statistical estimation
research. This talk is based on joint work with Jasper C.H. Lee.

Host: *Madhur Tulsiani* <madhurt at ttic.edu>

For more information on the *C**olloquium** Series* or to subscribe to the
mailing list, please see http://www.ttic.edu/colloquium.php




Mary C. Marre
Faculty Administrative Support
*Toyota Technological Institute*
*6045 S. Kenwood Avenue, Rm 517*
*Chicago, IL  60637*
*773-834-1757*
*mmarre at ttic.edu <mmarre at ttic.edu>*
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