
Communications and Signal Processing Seminar
Approximate independence of permutation mixtures
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Abstract: prove bounds on statistical distances between high-dimensional exchangeable mixture distributions (which we call \emph{permutation mixtures}) and their i.i.d. counterparts. Our results are based on a novel method for controlling $\chi^2$ divergences between exchangeable mixtures, which is tighter than the existing methods of moments or cumulants. At a technical level, a key innovation in our proofs is a new Maclaurin-type inequality for elementary symmetric polynomials of variables that sum to zero and an upper bound on permanents of doubly-stochastic positive semidefinite matrices. Our results imply an capacity upper bound for the noisy permutation channel, a de Finetti-style theorem (in the language of Diaconis and Freedman, 1987), and general asymptotic results for compound decision problems which generalize and strengthen a result of Hannan and Robbins (1955).
Based on a joint work (https://arxiv.org/abs/2408.09341) with Jonathan Niles-Weed.
Bio: Yanjun Han is an assistant professor of mathematics and data science at the Courant Institute of Mathematical Sciences and the Center for Data Science, New York University. He received his Ph.D. in Electrical Engineering from Stanford University in Aug 2021, under the supervision of Tsachy Weissman. After that, he spent one year as a postdoctoral scholar at the Simons Institute for the Theory of Computing, UC Berkeley, and another year as a Norbert Wiener postdoctoral associate in the Statistics and Data Science Center at MIT, mentored by Sasha Rakhlin and Philippe Rigollet. His research interests include high-dimensional and nonparametric statistics, bandits, and information theory.
*** The event will take place in a hybrid format. The location for in-person attendance will be room 3427 EECS. Attendance will also be available via Zoom.
Join Zoom Meeting: https://umich.zoom.us/j/93679028340
Meeting ID: 936 7902 8340
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Zoom Passcode information is available upon request to Kristi Rieger ([email protected]).