K E Y N O T E / I N V I T E D S P E A K E R S

**Peter Hall’s lecture**

### James Stephen Marron

Amos Hawley Professor of Statistics and Operations Research

UNC Gillings School OF Global Public Health

**Title: **Peter Hall and High Dimension Low Sample Size Asymptotics

**Abstract: **S. Marron is the Amos Hawley Distinguished Professor of Statistics and Operations Research, Professor of Biostatistics and Adjunct Professor of Computer Science at the University of North Carolina, Chapel Hill. His research lies in many areas statistics, data science and machine learning, with a special emphasis on gaining simultaneous insights from very diverse data types, including genomics, genetics, imaging and demographics. He enjoys using deep concepts from diverse mathematical areas including geometry and topology in novel data analyses.

**Bio:** J. S. Marron is the Amos Hawley Distinguished Professor of Statistics and Operations Research, Professor of Biostatistics and Adjunct Professor of Computer Science at the University of North Carolina, Chapel Hill. His research lies in many areas statistics, data science and machine learning, with a special emphasis on gaining simultaneous insights from very diverse data types, including genomics, genetics, imaging and demographics. He enjoys using deep concepts from diverse mathematical areas including geometry and topology in novel data analyses.

**Keynote Speakers**

**Title:** Estimation of the Distribution of Episodically Consumed Foods Measured with Error

**Abstract:** Dietary data collected from 24-hour dietary recalls are observed with significant measurement errors, in the sense that they are imprecise measurements of the long term intake of nutrients. In the nonparametric curve estimation literature, a lot of effort has been devoted to designing methods that are consistent under contamination by noise. However, some foods such as alcohol or fruits are consumed only episodically, and may not be consumed during the day when the 24-hour recall is administered. If the food is consumed on data collection day, the reported intake behaves like a contaminated version of a latent variable related to usual intake; if the food is not consumed on data collection day, the reported intake is equal to zero. For example, in the 2011–2013 Australian Health Survey, more than 5\% of the reported intakes of folic acid, caffeine and alcohol were equal to zero. Such data can be represented by a two part model, for which parametric techniques are well established, such as the National Cancer Institute approach. However, existing nonparametric errors-in-variables methods cannot deal with the excess zeros present in the data. We present new estimators of the distribution of such episodically consumed food data.

**Bio: **Aurore Delaigle is a professor of statistics at the University of Melbourne and co editor-in-chief of the Journal of the Royal Statistical Society, B. She is a member of the Australian Academy of Science and associate member of the Royal Academy of Science, Letters and Fine Arts of Belgium. Previously she held two research fellowships from the Australian Research Council, and held positions at the University of California at Davis and San Diego, and at the University of Bristol. Her main research areas are measurement errors, nonparametric statistics and functional data analysis.

**Title:** Non-parametric estimation for reinforcement learning

**Abstract: **Reinforcement learning (RL) consists of statistical procedures that use data to determine near-optimal policies for sequential decision-making. It makes use of Markov decision processes, and has applications in numerous areas (e.g., environmental control, robotics, supply chain management, competitive game-playing, industrial process control).

Non-parametric methods have a central role to play in this setting, but the RL setting brings several challenges that are not present for “static” non-parametric estimation problems, including the role of the Markovian dynamics and the challenges of off-policy data. In this talk, we provide an overview of these challenges, and discuss some recent progress, including non-asymptotic guarantees for procedures based on kernel methods, as well as non-parametric forms of Bellman residual and projection methods.

Based on joint research with: Yaqi Duan, Mengdi Wang and Andrea Zanette.

**Bio: **Martin Wainwright is currently the Howard Friesen Professor at the University of California at Berkeley, with a joint appointment between the Department of Statistics and the Department of EECS. He received a Bachelor’s degree in Mathematics from University of Waterloo, Canada, and Ph.D. degree in EECS from Massachusetts Institute of Technology (MIT).

His research interests include high-dimensional statistics, statistical machine learning, and reinforcement learning and sequential decision-making. Among other awards, he has received the COPSS Presidents’

Award (2014) from the Joint Statistical Societies; the David Blackwell Lectureship (2017) and Medallion Lectureship (2013) from the Institute of Mathematical Statistics; and Best Paper awards from the IEEE Signal Processing Society and IEEE Information Theory Society. He was a Section Lecturer at the International Congress of Mathematicians in 2014.

**Title:** Statistical Learning of Multivariate Extremes

**Abstract:** A spectral clustering algorithm for analyzing the dependence structure of multivariate extremes is proposed. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure in the multivariate regular variation setting. Our work studies the theoretical performance of spectral clustering based on a random k-nearest neighbor graph constructed from an extremal sample, i.e., the angular part of random vectors for which the radius exceeds a large threshold. In particular, we derive the asymptotic distribution of extremes arising from a linear factor model and prove that, under certain conditions, spectral clustering can consistently identify the clusters of extremes arising in this model. Leveraging this result we propose a simple consistent estimation strategy for learning the angular measure. Our theoretical findings are complemented with numerical experiments illustrating the finite sample performance of our methods. (This is joint work with Marco Avella Medina and Gennady Samorodnitsky.)

**Bio: **Richard Davis is the Howard Levene Professor of Statistics at Columbia University and former chair of the Statistics Department (2013-19). He has held academic positions at MIT, Colorado State University, and visiting appointments at numerous other universities. He was Hans Fischer Senior Fellow at the Technical University of Munich ( 2009-12) , Villum Kan Rasmussen Visiting Professor at the University of Copenhagen (2011-13), and Jubilee Professor at Chalmers University (2019). Davis is a fellow of the Institute of Mathematical Statistics and the American Statistical Association, and is an elected member of the International Statistical Institute. He was president of IMS in 2016 and Editor-in-Chief of Bernoulli Journal 2010-12. He is co-author (with Peter Brockwell) of the best-selling books, Time Series: Theory and Methods, Introduction to Time Series and Forecasting, and the time series analysis computer software package, ITSM2000. Together with Torben Andersen, Jens-Peter Kreiss, and Thomas Mikosch, he co-edited the Handbook in Financial Time Series and with Holan, Lund, and Ravishanker, the book, Handbook of Discrete-Valued Time Series. In 1998, he won (with collaborator W.T.M Dunsmuir) the Koopmans Prize for Econometric Theory. His research interests include time series, applied probability, extreme value theory, and spatial-temporal modeling.

**Special Invited Speakers**

**Title:** Long Story Short: Omitted Variable Bias in Causal Machine Learning

**Abstract: **We derive general, yet simple, sharp bounds on the size of the omitted variable bias for a broad class of causal parameters that can be identified as linear functionals of the conditional expectation function of the outcome. Such functionals encompass many of the traditional targets of investigation in causal inference studies, such as, for example, (weighted) average of potential outcomes, average treatment effects (including subgroup effects, such as the effect on the treated), (weighted) average derivatives, and policy effects from shifts in covariate distribution — all for general, nonparametric causal models. Our construction relies on the Riesz-Frechet representation of the target functional. Specifically, we show how the bound on the bias depends only on the additional variation that the latent variables create both in the outcome and in the Riesz representer for the parameter of interest. Moreover, in many important cases (e.g, average treatment effects and average derivatives) the bound is shown to depend on easily interpretable quantities that measure the explanatory power of the omitted variables. Therefore, simple plausibility judgments on the maximum explanatory power of omitted variables (in explaining treatment and outcome variation) are sufficient to place overall bounds on the size of the bias. Furthermore, we use debiased machine learning to provide flexible and efficient statistical inference on learnable components of the bounds. Finally, empirical examples demonstrate the usefulness of the approach.

**Bio: **Victor Chernozhukov is the International Ford Professor in the Department of Economics at MIT and Center for Statistics and Data Science of MIT. He received his Ph.D. from Stanford University in 2000, and has worked at MIT since then. He works primarily in econometrics and mathematical statistics, with much of recent work focusing on the causal inference using machine learning methods. He is a fellow of The Econometric Society and a recipient of The Alfred P. Sloan Research Fellowship, The Arnold Zellner Award, and The Bessel Award. He was elected to the American Academy of Arts and Sciences in 2016 and a Fellow of the Institute of Mathematical Statistics in 2019.

**Title:** Problems in network archaeology: root finding and broadcasting

**Abstract:** Networks are often naturally modeled by random processes in which nodes of the network are added one-by-one, according to some random rule. Uniform and preferential attachment trees are among the simplest examples of such dynamically growing networks. The statistical problems we address in this talk regard discovering the past of the network when a present-day snapshot is observed. We present a few results that show that, even in gigantic networks, a lot of information is preserved from the very early days. In particular, we discuss the problem of finding the root and the broadcasting problem.

**Bio:** Gabor Lugosi is an ICREA research professor at the Department of Economics, Pompeu Fabra University, Barcelona. His research main interests include the theory of machine learning, combinatorial statistics, inequalities in probability, random graphs and random structures, and information theory.

**Title:** Bayesian non-linear inverse problems: progress and challenges

**Abstract:** Common examples for non-linear inverse problems range from parameter identification in PDEs to tomography and data assimilation problems. They naturally involve high- or infinite dimensional parameter spaces and appropriate statistical noise models lead to a class of non-convex inference problems that present substantial challenges in contemporary data science. In influential work, Andrew Stuart (2010) has proposed a unified Bayesian approach to solve such problems. It is computationally feasible via Gaussian process priors and high-dimensional MCMC algorithms and provides important uncertainty quantification methodology (‘error bars’ or confidence regions) based on posterior distributions. Despite evident empirical success, the theoretical understanding of the performance of such methods has been limited until recently. Specifically in non-linear settings Bayesian methods are distinct from optimisation based algorithms and their analysis requires a very different set of mathematical ideas. We will summarise recent developments that allow to give rigorous statistical and computational guarantees for the use of these algorithms.

**Bio:** Richard Nickl is Professor of Mathematical Statistics at the University of Cambridge, UK. His mathematical contributions have been widely recognised, e.g., as invited speaker at the International Congress of Mathematicians in 2022 and at the European Congress of Mathematics 2021; he has also been awarded the 2017 Ethel Newbold prize of the Bernoulli Society and the 2017 PROSE award in mathematics for his monograph `Mathematical foundations of infinite dimensional statistical models’ published by Cambridge University Press.