Thanks are due to our colleague, Vladimir Koltchinskii, for arranging this visit. Please write to Vladimir if you would like to meet with Professor Gabor Lugosi during his visit, or for additional information.
In these lectures we discuss some statistical problems with an interesting combinatorial structure behind. We start by reviewing the "hidden clique" problem, a simple prototypical example with a surprisingly rich structure. We also discuss various "combinatorial" testing problems and their connections to high-dimensional random geometric graphs. Time permitting, we study the problem of estimating the mean of a random variable.