Abstract: Wasserstein-based distributional robust optimization problems are formulated as min-max games in which a statistician chooses a parameter to minimize an expected loss against an adversary (say nature) which wishes to maximize the loss by choosing an appropriate probability model within a certain non-parametric class. Recently, these formulations have been studied in the context in which the non-parametric class chosen by nature is defined as a Wasserstein-distance neighborhood around the empirical measure. It turns out that by appropriately choosing the…

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 this as 'double dipping'. Unfortunately, double dipping can lead to highly-inflated Type 1 errors. In this talk, I will consider the special case of hierarchical…

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 these questions change from "extremely likely" to "extremely unlikely," and moreover we give a simple characterization of this threshold for different properties. Our motivation comes…

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 Rejection Sampling relies on a high-dimensional proposal distribution built using ensembles of state samples and dynamic programming. Although this algorithm can be interpreted as a…

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 move much, or require large number of neurons. In this paper we develop a local convergence theory for mildly over-parameterized two-layer neural net. We show…