Title: 

Modern Sampling Paradigms: from Posterior Sampling to Generative AI

Abstract: 

Sampling from a target distribution is a recurring theme in statistics and generative artificial intelligence (AI). In statistics, posterior sampling offers a flexible inferential framework, enabling uncertainty quantification, probabilistic prediction, as well as the estimation of intractable quantities. In generative AI, sampling aims to generate unseen instances that emulate a target population, such as the natural distributions of texts, images, and molecules. 

In this talk, I will present my works on designing provably efficient sampling algorithms, addressing challenges in both statistics and generative AI. (1) In the first part, I will focus on posterior sampling for Bayes sparse regression. In general, such posteriors are high-dimensional and contain many modes, making them challenging to sample from. To address this, we develop a novel sampling algorithm based on decomposing the target posterior into a log-concave mixture of simple distributions, reducing sampling from a complex distribution to sampling from a tractable log-concave one. We establish provable guarantees for our method in a challenging regime that was previously intractable. (2) In the second part, I will describe a training-free acceleration method for diffusion models, which are deep generative models that underpin cutting-edge applications such as AlphaFold, DALL-E and Sora. Our approach is simple to implement, wraps around any pre-trained diffusion model, and comes with a provable convergence rate that strengthens prior theoretical results. We demonstrate the effectiveness of our method on several real-world image generation tasks. 

Lastly, I will outline my vision for bridging the fields of statistics and generative AI, exploring how insights from one domain can drive progress in the other.

Bio: 

Yuchen Wu is a departmental postdoctoral researcher in the Department of Statistics and Data Science at the Wharton School, University of Pennsylvania. She earned her Ph.D. in 2023 from Stanford University, where she was advised by Professor Andrea Montanari. Her research lies broadly at the intersection of statistics and machine learning, featuring generative AI, high-dimensional statistics, Bayesian inference, algorithm design, and data-driven decision making.