Abstract: In this work we consider bootstrap-based inference methods for functions of the parameter vector in the presence of many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n. In particular this covers the case of subvector inference, such as the inference on a…
Abstract: The talk will focus on optimization on the high-dimensional sphere when the objective function is a linear combination of homogeneous polynomials with standard Gaussian coefficients. Such random processes are called spherical spin glasses in physics, and have been extensively studied since the 80s. I will describe certain geometric properties of spherical spin glasses unique…
Abstract: This talk will present a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fruitful to formulate exponential concentration inequalities in this way. We will illustrate this point by presenting a single assumption and a single theorem…
Logistic regression is a fundamental task in machine learning and statistics. For the simple case of linear models, Hazan et al. (2014) showed that any logistic regression algorithm that estimates model weights from samples must exhibit exponential dependence on the weight magnitude. As an alternative, we explore a counterintuitive technique called improper learning, whereby one…
Abstract: Chao Gao will discuss the problem of statistical estimation with contaminated data. In the first part of the talk, I will discuss depth-based approaches that achieve minimax rates in various problems. In general, the minimax rate of a given problem with contamination consists of two terms: the statistical complexity without contamination, and the contamination…
Abstract: We consider the problem of efficient sampling from the hard-core and Potts models from statistical physics. On certain families of graphs, phase transitions in the underlying physics model are linked to changes in the performance of some sampling algorithms, including Markov chains. We develop new sampling and counting algorithms that exploit the phase transition…
Abstract: We first study the rate of convergence for learning distributions with the adversarial framework and Generative Adversarial Networks (GANs), which subsumes Wasserstein, Sobolev, and MMD GANs as special cases. We study a wide range of parametric and nonparametric target distributions, under a collection of objective evaluation metrics. On the nonparametric end, we investigate the…
Abstract: The problem of transfer and domain adaptation is ubiquitous in machine learning and concerns situations where predictive technologies, trained on a given source dataset, have to be transferred to a new target domain that is somewhat related. For example, transferring voice recognition trained on American English accents to apply to Scottish accents, with minimal…
Abstract: What are the most expressive classes of neural networks that can be learned, provably, in polynomial-time in a distribution-free setting? In this talk we give the first efficient algorithm for learning neural networks with two nonlinear layers using tools for solving isotonic regression, a nonconvex (but tractable) optimization problem. If we further assume the…