## October 2019

## Towards Robust Statistical Learning Theory

Stanislav Minsker (University of Southern California)

E18-304

Abstract: Real-world data typically do not fit statistical models or satisfy assumptions underlying the theory exactly, hence reducing the number and strictness of these assumptions helps to lessen the gap between the “mathematical” world and the “real” world. The concept of robustness, in particular, robustness to outliers, plays the central role in understanding this gap. The goal of the talk is to introduce the principles and robust algorithms based on these principles that can be applied in the general framework of statistical…

Find out more »## The Planted Matching Problem

Cristopher Moore (Santa Fe Institute)

E18-304

Abstract: What happens when an optimization problem has a good solution built into it, but which is partly obscured by randomness? Here we revisit a classic polynomial-time problem, the minimum perfect matching problem on bipartite graphs. If the edges have random weights in , Mézard and Parisi — and then Aldous, rigorously — showed that the minimum matching has expected weight zeta(2) = pi^2/6. We consider a “planted” version where a particular matching has weights drawn from an exponential distribution…

Find out more »## September 2019

## Frontiers of Efficient Neural-Network Learnability

Adam Klivans (University of Texas at Austin)

E18-304

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 distribution is symmetric, we obtain the first efficient algorithm for recovering the parameters of a one-layer convolutional network. These results implicitly make use of a…

Find out more »## Some New Insights On Transfer Learning

Samory Kpotufe (Columbia University)

E18-304

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 retraining. A first challenge is to understand how to properly model the ‘distance’ between source and target domains, viewed as probability distributions over a feature…

Find out more »## GANs, Optimal Transport, and Implicit Density Estimation

Tengyuan Liang (University of Chicago)

E18-304

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 minimax optimal rates and fundamental difficulty of the implicit density estimation under the adversarial framework. On the parametric end, we establish a theory for general…

Find out more »## May 2019

## Counting and sampling at low temperatures

Will Perkins (University of Illinois at Chicago)

E18-304

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 phenomenon and work efficiently on lattices (and bipartite expander graphs) at sufficiently low temperatures in the phase coexistence regime. Our algorithms are based on Pirogov-Sinai…

Find out more »## Stochastics and Statistics Seminar Series

Tracy Ke (Harvard University)

E18-304

## April 2019

## Robust Estimation: Optimal Rates, Computation and Adaptation

Chao Gao (University of Chicago)

E18-304

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 effect in the form of modulus of continuity. In the second part of the talk, I will discuss computational challenges of these depth-based estimators. An…

Find out more »## Stochastics and Statistics Seminar Series

Dylan Foster (MIT)

E18-304

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 estimates a linear model by fitting a non-linear model. Past success stories for improper learning have focused on cases where it can improve computational complexity.…

Find out more »## Exponential line-crossing inequalities

Aaditya Ramdas (Carnegie Mellon University)

E18-304

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 that together strengthen many tail bounds for martingales, including classical inequalities (1960-80) by Bernstein, Bennett, Hoeffding, and Freedman; contemporary inequalities (1980-2000) by Shorack and Wellner,…

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