Schedule for Fall 2024

9/11/2024

Speaker: Professor Andrew Gelman

Title: Modeling Weights to Generalize

Abstract: A well-known rule in practical survey research is to include weights when estimating a population average but not to use weights when fitting a regression model—as long as the regression includes as predictors all the information that went into the sampling weights. But what if you don’t know where the weights came from? We propose a quasi-Bayesian approach using a joint regression of the outcome and the sampling weight, followed by poststratifcation on the two variables, thus using design information within a model-based context to obtain inferences for small-area estimates, regressions, and other population quantities of interest. For background, see here:

 http://www.stat.columbia.edu/~gelman/research/unpublished/weight_regression.pdf

9/18/2024

Speakers: Dr. Julien Boussard and Dr. Collin Cademartori

Title: Experiences of recent graduates

Abstract: Recent graduates will share their research journey across their PhD and other valuable insights. Both speakers will start by giving a brief overview of their journey through graduate school, and their research, placing emphasis on lessons learnt through the process and what they would have done differently if they were to begin graduate school again.
Collin will elaborate on his journey from the beginnings of research to starting his current position as an assistant professor at Wake Forest. This talk will probably be most relevant to those of you who are interested in applying for academic jobs and who have at least some interest in teaching, since these are the factors that most strongly influenced his job market experience. Julien will also focus on the specifics of doing applied statistical research (as opposed to theoretical research), and try to give some advice for students interested in applied research. He will also talk briefly about the process of finding a postdoc.

9/25/2024

Speaker: Prof. Gitta Kutyniok from LMU Munich

Title: Reliable AI: Successes, Limitations, and Next Generation Computing

Abstract: The new wave of artificial intelligence is impacting industry, public life, and the sciences in an unprecedented manner. However, one current major drawback is the lack of reliability as well as the enormous energy problem of AI.
The goal of this lecture is to first provide an introduction into this new vibrant research area, and showcase some recent successes. We will then focus on limitations of reliability of AI from a mathematical perspective, in particular, with respect to computability problems caused by current (digital) hardware. This will lead us naturally to novel approaches for future AI computing such as neuromorphic computing and spiking neural networks as the associated type of neural networks.

10/2/2024

Speaker: Prof. Nicolas Garcia Trillos

Title: The shape of adversarial training

Abstract: This talk is about two apparently non-overlapping stories. One story is about shapes in space (Euclidean space or a network), their perimeter, their curvature, and about a new notion of Wasserstein barycenters. The other story is about machine learning, specifically about how to train learning models to be robust to adversarial perturbations of data. The bigger story in the talk will be about how these two stories interact with each other, how adversarial robustness motivates new notions of perimeter and curvature, and how geometry and optimal transport can cast new lights on and in this way reveal new faces of an important task in machine learning.

10/9/2024

Speaker: Prof. Christopher Harshaw

Title: Estimating Direct Effects under Interference: a Spectral Approach to Experimental Design

Abstract: From clinical trials to corporate strategy, randomized experiments are a reliable methodological tool for estimating causal effects. In recent years, there has been a growing interest in causal inference under interference, where treatment given to one unit can affect outcomes of other units. While the literature on interference has focused primarily on unbiased and consistent estimation, designing randomized network experiments to insure tight rates of convergence is relatively under-explored for many settings.

In this talk, we study the problem of direct effect estimation under interference. Here, the interference between experimental subjects is captured by a network and the experimenter seeks to estimate the direct effect, which is the difference between the outcomes when (i) a unit is treated and its neighbors receive control and (ii) the unit and its neighbors receive control. We present a new experimental design under which the normalized variance of a Horvitz—Thompson style estimator is bounded as $n * Var <= O( \lambda )$, where $\lambda$ is the largest eigenvalue of the adjacency matrix of the graph. This experimental approach achieves consistency when $\lambda = o(n)$, which is a much weaker condition on the network than most similar approaches which require the maximum degree to be bounded. This experimental design, which relies on insights from spectral graph theory, establishes the best known rate of convergence for this problem; in fact, we offer lower bounds for any experimental design, which match our rates in certain instances. In addition, we present a variance estimator and CLT which facilitate the construction of asymptotically valid confidence intervals. Finally, simulations using data from a real network experiment corroborate the theoretical claims.

10/16/2024

Title: Summer internship experiences of current students

The following students will share their experiences about their summer internship.

1. Ling Chen, Tudor Investment Corporation (high frequency trading team)
2. Irene 

10/23/2024

Speaker: Prof. Bodhi Sen (Columbia University)

Title: A New Perspective On Denoising Based On Optimal Transport

Abstract: In the standard formulation of the denoising problem, one is given a probabilistic model relating a latent variable and an observation Z, and the goal is to construct a map to recover the latent variable from Z. The posterior mean, a natural candidate for estimating the latent variable from observation, attains the minimum Bayes risk (under the squared error loss) but at the expense of over-shrinking the Z, and in general may fail to capture the geometric

features of the latent variable distribution (e.g., low dimensionality, discreteness, sparsity, etc.). To rectify these drawbacks, we develop a new perspective on this denoising problem that is inspired by optimal transport (OT) theory and use it to propose a new OT-based denoiser at the population level setting. We rigorously prove that, under general assumptions on the model, our OT-based denoiser is well-defined and unique, and is closely connected to solutions to a Monge OT problem. Under appropriate identifiability assumptions on the model, our OT-based denoiser can be recovered solely from information of the marginal distribution of Z and the posterior mean of the model, after solving a linear relaxation problem over a suitable space of couplings that is reminiscent of a standard multi-marginal OT (MOT) problem. I will also mention its connections to empirical Bayes and compound decision theory. This is joint work with Nicolas Garcia Trillos (U Wisconsin).

10/30/2024

Speaker: Prof. Cynthia Rush (Columbia University)

Title:  Approximate Message Passing for High-Dimensional Estimation and Inference

Abstract: Approximate Message Passing (AMP) refers to a class of efficient, iterative algorithms that have been applied in a number of statistical problems, such as linear regression, generalized linear models and low-rank matrix estimation. Moreover, this class of algorithms is popular and practical for use in many engineering applications, including imaging, communications and deep learning.  The broad goal of this talk is to provide a mathematical introduction to AMP and a recipe for how to use AMP theory to establish precise asymptotic guarantees for a variety of statistical procedures (e.g., spectral methods, LASSO, $L_1$ interpolation) in the high-dimensional regime, under suitable assumptions on the data.

11/6/2024

Speaker: Arian Maleki

Title: High-dimensional Asymptotic Analysis: Opportunities and Challenges

Abstract: A cornerstone of estimation theory is asymptotic analysis, where the number of observations n is assumed to go to infinity while the number of parameters remains fixed. Under these classical asymptotic settings, many influential results, such as the optimality of the maximum likelihood estimator (MLE), have been established. However, in many emerging applications-from biology to artificial intelligence-the number of features or parameters and the number of observations are both large. In some cases, p is even larger than n. This violates the assumption of classical asymptotic theory where p/n \to 0, rendering classical results, like the optimality of MLE, inaccurate in these high-dimensional settings. The field of 'high-dimensional asymptotics' seeks to replace the classical asymptotic framework with one suited for high-dimensional scenarios. In my talk, I will briefly introduce some of these high-dimensional asymptotic frameworks and discuss the opportunities they offer for advancing real-world applications. If time permits, I will also highlight some open problems, with a particular focus on those that our group is actively exploring.

11/13/2024

Speakers: Genevera Allen, John Cunningham, Liam Paninski and Lea Duncker

Title: Zuckerman Institute Panel talk

Abstract:  This week four professors associated with the Zuckerman Institute and with research at the intersection of neural data and statistics are invited in a discussion-style seminar. The discussion will be focused on their current research and how they foster interdisciplinary collaboration within the institute.

11/20/2024

Speaker: Mohammadreza Kalan - Joint work with Samory Kpotufe

Title: Transfer Learning in Outlier Detection

Abstract:  A critical barrier to learning an accurate decision rule for outlier detection is the scarcity of outlier data. As such, practitioners often turn to similar but imperfect outlier data, from which they might transfer information to the target outlier detection task. While transfer learning has been extensively considered in traditional classification, the problem of transfer in outlier detection, and more generally in unbalanced classification settings, has received less attention. In this work, we adopt the traditional framework of Neyman-Pearson classification, which formalizes supervised outlier detection, and determine the information-theoretic limits of the problem under a measure of discrepancy. We show that, unlike traditional classification, it yields distinct fast and slow minimax rates. Furthermore, we propose a transfer learning algorithm for outlier detection that is amenable to practical implementation.

11/27/2024

12/4/2024

12/11/2024

12/18/2024