Tail inference

Tuesday, April 28, 2015 - 3:20pm - 4:10pm
Steven Heilman (University of California, Los Angeles)
We study contraction under a Markov semi-group and influence bounds for functions all of whose low level Fourier coefficients vanish. This study is motivated by the explicit construction of 3-regular expander graphs of Mendel and Naor, though our results have no direct implication for the construction of expander graphs.
Friday, April 17, 2015 - 9:00am - 9:50am
Roberto Oliveira (Institute of Pure and Applied Mathematics (IMPA))
Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the lower tail of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the one-dimensional marginals of the random vectors. A similar result holds for more general sums of random positive semidefinite matrices and the (relatively simple) proof uses a variant of the so-called PAC-Bayesian method for bounding empirical processes.
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