Stochastics and Statistics Seminar

Abstract: Energy-based models are a recent class of probabilistic generative models wherein the distribution being learned is parametrized up to a constant of proportionality (i.e. a partition function). Fitting such models using maximum likelihood (i.e. finding the parameters which maximize the probability of the observed data) is computationally challenging, as evaluating the partition function involves a high dimensional integral. Thus, newer incarnations of this paradigm instead train other losses which obviate the need to evaluate partition functions. Prominent examples include score matching (in which we fit…

Abstract: The Paley graph is a classical number-theoretic construction of a graph that is believed to behave "pseudorandomly" in many regards. Accurately bounding the clique number of the Paley graph is a long-standing open problem in number theory, with applications to several other questions about the statistics of finite fields. I will present recent results studying the application of convex optimization and spectral graph theory to this problem, which involve understanding the extent to which the Paley graph is "spectrally…

Abstract: Sampling from high-dimensional probability distributions is a fundamental and challenging problem encountered throughout science and engineering. One of the most popular approaches to tackle such problems is the Markov chain Monte Carlo (MCMC) paradigm. While MCMC algorithms are often simple to implement and widely used in practice, analyzing the rate of convergence to stationarity, i.e. the "mixing time", remains a challenging problem in many settings. I will describe a new technique based on pairwise correlations called "spectral independence", which has been…

Abstract: In this talk I will propose new tools for the exploratory data analysis of data objects taking values in a general separable metric space. First, I will introduce depth profiles, where the depth profile of a point ω in the metric space refers to the distribution of the distances between ω and the data objects. I will describe how depth profiles can be harnessed to define transport ranks, which capture the centrality of each element in the metric space with respect to the…

Abstract: Regression discontinuity design (RDD) is a quasi-experimental impact evaluation method ubiquitous in the social- and applied health sciences. It aims to estimate average treatment effects of policy interventions by exploiting jumps in outcomes induced by cut-off assignment rules. Here, we establish a correspondence between the RDD setting and free discontinuity problems, in particular the celebrated Mumford-Shah model in image segmentation. The Mumford-Shah model is non-convex and hence admits local solutions in general. We circumvent this issue by relying on…

Abstract: This talk is based on two recent papers: 1. “On the Pointwise Behavior of Recursive Partitioning and Its Implications for Heterogeneous Causal Effect Estimation” and 2. “Convergence Rates of Oblique Regression Trees for Flexible Function Libraries” 1. Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of experiments, where tree estimation and inference is conducted at specific values of…

Abstract: In this talk, I will argue that it is sometimes possible to learn, with techniques originated from bandits, the "hints" on which learning-augmented algorithms rely to improve worst-case performances. We will describe this phenomenon, the combination of online learning with competitive analysis, on the example of stochastic online scheduling. We shall quantify the merits of this approach by computing and comparing non-asymptotic expected competitive ratios (the standard performance measure of algorithms) Bio: Vianney Perchet is a professor at the…

Abstract: The low-degree polynomial framework has emerged as a versatile tool for probing the computational complexity of statistical problems by studying the power and limitations of a restricted class of algorithms: low-degree polynomials. Focusing on the setting of hypothesis testing, I will discuss some extensions of this method that allow us to tackle finer-grained questions than the standard approach. First, for the task of detecting a planted clique in a random graph, we ask not merely when this can be…