## Past Events › Stochastics and Statistics Seminar Series

The MIT Statistics and Data Science Center hosts guest lecturers from around the world in this weekly seminar.

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## Stochastics and Statistics Seminar Series

Dylan Foster (MIT)

E18-304

<strong style="color: #acc936;"> Abstract: </strong> 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…

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,…

Find out more »## Optimization of random polynomials on the sphere in the full-RSB regime

Eliran Subag (New York University)

E18-304

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 to the full-RSB case, and explain how they can be used to design a polynomial time algorithm that finds points within small multiplicative error from…

Find out more »## Subvector Inference in Partially Identified Models with Many Moment Inequalities

Alex Belloni (Duke University)

E18-304

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 single component associated with a treatment/policy variable of interest. We consider a min-max of (centered and non-centered) Studentized statistics and study the properties of the…

Find out more »## Univariate total variation denoising, trend filtering and multivariate Hardy-Krause variation denoising

Aditya Guntuboyina (UC Berkley)

E18-304

Abstract: Total variation denoising (TVD) is a popular technique for nonparametric function estimation. I will first present a theoretical optimality result for univariate TVD for estimating piecewise constant functions. I will then present related results for various extensions of univariate TVD including adaptive risk bounds for higher-order TVD (also known as trend filtering) as well as a multivariate extension via the Hardy-Krause Variation which avoids the curse of dimensionality to some extent. I will also mention connections to shape restricted…

Find out more »## Why Aren’t Network Statistics Accompanied By Uncertainty Statements?

Eric Kolaczyk (Boston University)

E18-304

Abstract: Over 500K scientific articles have been published since 1999 with the word “network” in the title. And the vast majority of these report network summary statistics of one type or another. However, these numbers are rarely accompanied by any quantification of uncertainty. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Perhaps surprisingly, there is little in the way of…

Find out more »## Capacity lower bound for the Ising perceptron

Nike Sun (MIT)

E18-304

Abstract: The perceptron is a toy model of a simple neural network that stores a collection of given patterns. Its analysis reduces to a simple problem in high-dimensional geometry, namely, understanding the intersection of the cube (or sphere) with a collection of random half-spaces. Despite the simplicity of this model, its high-dimensional asymptotics are not well understood. I will describe what is known and present recent results. This is joint work with Jian Ding. Biography: Nike Sun is a faculty…

Find out more »## TAP free energy, spin glasses, and variational inference

Zhou Fan (Yale University)

E18-304

Abstract: We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is equivalent to the Bayesian posterior for a high-dimensional estimation problem known as "Z2 synchronization". Statistical physics suggests to compute the expectation with respect to this Gibbs measure (the posterior mean in the synchronization problem), by minimizing the so-called Thouless-Anderson-Palmer (TAP) free energy, instead of the mean field (MF) free energy. We prove that this identification…

Find out more »## Medical Image Imputation

Polina Golland (MIT CSAIL)

E18-304

Abstract: We present an algorithm for creating high resolution anatomically plausible images that are consistent with acquired clinical brain MRI scans with large inter-slice spacing. Although large databases of clinical images contain a wealth of information, medical acquisition constraints result in sparse scans that miss much of the anatomy. These characteristics often render computational analysis impractical as standard processing algorithms tend to fail when applied to such images. Our goal is to enable application of existing algorithms that were originally…

Find out more »## Optimization of the Sherrington-Kirkpatrick Hamiltonian

Andrea Montanari (Stanford University )

E18-304

Andrea Montanari Professor, Department of Electrical Engineering, Department of Statistics Stanford University This lecture is in conjunction with the LIDS Student Conference. Abstract: Let A be n × n symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the problem of maximizing xT Ax over binary vectors with ±1 entries. In the language of statistical physics, this amounts to finding the ground state of the Sherrington-Kirkpatrick model of spin glasses. The asymptotic value of this…

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