Abstract:  As datasets continue to grow in size, in many settings the focus of data collection has shifted away from testing pre-specified hypotheses, and towards hypothesis generation. Researchers are often interested in performing an exploratory data analysis in order to generate hypotheses, and then testing those hypotheses on the same data; I will refer to…

Abstract: What combinatorial properties are likely to be satisfied by a random subspace over a finite field? For example, is it likely that not too many points lie in any Hamming ball? What about any cube?  We show that there is a sharp threshold on the dimension of the subspace at which the answers to…

Abstract: I will introduce Ensemble Rejection Sampling, a scheme for perfect simulation of a class of Feynmac-Kac models. In particular, this scheme allows us to sample exactly from the posterior distribution of the latent states of a class of non-linear non-Gaussian state-space models and from the distribution of a class of conditioned random walks. Ensemble…

Abstract: The training of neural networks optimizes complex non-convex objective functions, yet in practice simple algorithms achieve great performances. Recent works suggest that over-parametrization could be a key ingredient in explaining this discrepancy. However, current theories could not fully explain the role of over-parameterization. In particular, they either work in a regime where neurons don't…