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Compressed Empirical Measures

Presented by: 
Steffen Grunewalder Lancaster University - Mathematics and Statistic Dept.
Thursday 29th March 2018 - 11:00 to 12:00
INI Seminar Room 2
I will present results on compressed representations of expectation operators with a particular emphasis on expectations with respect to empirical measures. Such expectations are a cornerstone of non-parametric statistics and compressed representations are of great value when dealing with large sample sizes and computationally expensive methods. I will focus on a conditional gradient like algorithm to generate such representations in infinite dimensional function spaces. In particular, I will discuss extensions of classical convergence results to uniformly smooth Banach spaces (think Lp, 1 < p < 1, or various scales of Besov and Sobolev spaces); a counter example to fast rates of convergence in norm when compact sets are used for approximations; workarounds based on slicing compact sets in suitable ways and a result about fast convergence when the norm convergence is replaced with a weaker form of convergence; results about the location of the representer of a probability measure inside the approximation set using smoothness assumptions on the point-evaluators; and an application of these results to empirical processes.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons