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…

Abstract: This talk will focus on gradient-based optimization of two-layer neural networks. We consider a high-dimensional setting where the number of samples and the input dimension are both large and show that, under different model assumptions, neural networks learn useful features and adapt to the model more efficiently than classical methods. Further, we derive scaling laws of the learning dynamics for the gradient descent, highlighting the power-law dependencies on the optimization time, and the model width. Bio: Murat A. Erdogdu…

TBD

Abstract: The widespread adoption of AI and machine learning models in in society has brought increased attention to how model predictions impact decision processes in a variety of domains. I will describe tools that apply statistical decision theory and information economics to address pressing question at the human-AI interface. These include: how to evaluate when a decision-maker appropriately relies on model predictions, when a human or AI agent could better exploit available contextual information, and how to evaluate (and design)…