Stochastics and Statistics Seminar

Abstract:  We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. By integrating concepts and tools from cross-validation and differential privacy, we develop a test statistic that is asymptotically normal even in high-dimensional settings, and allows for arbitrarily many ties in the population mean vector. The key technical ingredient is a central limit theorem for globally dependent data characterized…

Abstract In this talk we will discuss statistical inference of average treatment effect in measured confounder settings as well as parallel questions of inferring linear and quadratic functionals in generalized linear models under high dimensional proportional asymptotic settings i.e. when p/n→δ∈(0,∞) where p, n denote the dimension of the covariates and the sample size respectively . The results rely on the knowledge of the variance covariance matrix Σ of the covariates under study and we show that whereas √n-consistent asymptotically…

Abstract:  Recent advances in AI have underscored that data, rather than model size, is now the primary bottleneck in large-scale machine learning performance. Yet, despite this shift, systematic methods for dataset curation, augmentation, and optimization remain underdeveloped. In this talk, I will argue for the need for a "Chemistry of AI"—a paradigm that, like the emerging "Physics of AI," embraces a principles-first, rigorous, empiricist approach but shifts the focus from models to data. This perspective treats datasets as structured, dynamic…

Abstract: This talk will address to recent projects I am excited about. The first describes efficient methodologies for hyper-parameter estimation in optimization algorithms. I will describe two approaches for how to adaptively estimate these parameters that often lead to significant improvement in convergence. The second describes a new method, called Metropolis-Adjusted Preconditioned Langevin Algorithm for sampling from a convex body. Taking an optimization perspective, I focus on the mixing time guarantees of these algorithms — an essential theoretical property for…

Abstract: Stein Variational Gradient Descent (SVGD) is a deterministic, interacting particle-based algorithm for nonparametric variational inference, yet its theoretical properties remain challenging to fully understand. This talk presents two complementary perspectives on SVGD. First, we introduce Gaussian-SVGD, a framework that projects SVGD onto the family of Gaussian distributions using a bilinear kernel. We establish rigorous convergence results for both mean-field dynamics and finite-particle systems, proving linear convergence to equilibrium in strongly log-concave settings. This framework also unifies recent algorithms for…

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