The Hotelling Lectures are an annual event in the Department of Statistics & Operations Research at the University of North Carolina – Chapel Hill, honoring the memory of Professor Harold Hotelling (first chairman of the “Department of Mathematical Statistics”, as it was originally named at the time of its inception in 1946). A distinguished guest speaker presents a series of talks (which are open to the public) and remains in residence at the Department for several days. The inaugural Hotelling Lectures were given by David R. Cox in 1980, followed in subsequent years by these other distinguished speakers: Herman Chernoff, Ole Barndorff-Nielsen, Frank Hampel, David Brillinger, David Kendall, Persi Diaconis, Pal Revesz, Willem van Zwet, C.R. Rao, Bradley Efron, Lucien LeCam, Peter Bickel, Ulf Grenander, Larry Shepp, David Donoho, David Siegmund, Herbert Robbins, Lawrence D. Brown, Nancy Reid, S.R.S. Varadhan, Stuart Geman, Iain Johnstone, Peter Hall, Ruth J. Williams, Terry Speed, Thomas Kurtz, Peter McCullagh, Richard Davis, Yuval Peres and Dimitris Bertsimas.

Structural Breaks, Outliers, MDL, Some Theory and Google Trends In this lecture, we will take another look at modeling time series that exhibit certain types of nonstationarity. Often one encounters time series for which segments look stationary, but the whole ensemble is nonstationary. On top of this, each segment of the data may be further contaminated by an unknown number of innovational and/or additive outliers; a situation that presents interesting modeling challenges. We will seek to find the best fitting…

Big n, Big p: Eigenvalues for Cov Matrices of Heavy-Tailed Multivariate Time Series In this paper we give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series when the number of components p goes to infinity with the sample size. The time series constitutes a linear process across time and between components. The input noise of the linear process has regularly varying tails with index between 0 and 4; in particular, the time…

Local Partitioning and hidden Cliques in Massive Graphs A local partitioning algorithm finds a "community" for a given node in a large graph (i.e., a set of nodes with relatively few bonds to the outside) by examining only a small part of the entire graph. I will describe the "evolving set" partitioning algorithm, developed jointly with Reid Andersen, which is based on earlier work with Ben Morris on mixing times for Markov chains. In the second part of the talk,…

Towards Optimal Algorithms for Prediction with Expert Advice We study the classical problem of prediction with expert advice in the adversarial setting with a geometric stopping time. Cover (1965) gave the optimal algorithm that minimizes worst-case regret for the case of 2 experts. In this talk, I will describe the optimal algorithm, adversary and regret for the case of 3 experts. We will see that optimal algorithm for 2 and 3 experts is a probability matching algorithm (analogous to Thompson…

Machine Learning and Statistics via a modern optimization lens The field of Statistics has historically been linked with Probability Theory. However, some of the central problems of classification, regression and estimation can naturally be written as optimization problems. While continuous optimization approaches has had a significant impact in Statistics, mixed integer optimization (MIO) has played a very limited role, primarily based on the belief that MIO models are computationally intractable. The period 1991–2015 has witnessed a) algorithmic advances in mixed…

From Predictive to Prescriptive Analytics Operations Research and Management Science (OR/MS) as a field typically starts with models and aims to obtain decisions. Data by enlarge is rarely present. Machine learning (ML)/ Statistics (S) as a field typically starts with data and aims to make predictions. Decisions are rarely addressed. In this work, we combine ideas from ML/S and OR/MS in developing a framework, along with specific methods, for using data to prescribe optimal decisions in OR/MS problems. In a…

Nonparametric Bayesian methods: frequentist analysis Aad van der Vaart Leiden University We present an overview of Bayesian methods to estimate functions or high-dimensional parameter vectors, and discuss the validity (or not) of these methods from a non-Bayesian point of view. For instance, we consider using a Gaussian process as a prior for a regression function or (after exponentiation and normalisation) for a density function. We characterise the rate at which the corresponding posterior distribution can recover a true function as…

Nonparametric Bayesian methods: frequentist analysis Aad van der Vaart Leiden University A more detailed view of Bayesian methods to estimate functions or high-dimensional parameter vectors, and discuss the validity (or not) of these methods from a non-Bayesian point of view. For instance, we consider using a Gaussian process as a prior for a regression function or (after exponentiation and normalisation) for a density function. We characterise the rate at which the corresponding posterior distribution can recover a true function as…