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Colloquium: Ye He (GeorgiaTech)

10 Feb @ 3:30 pm - 4:30 pm

Colloquium: Ye He (GeorgiaTech)

10 Feb @ 3:30 pm – 4:30 pm
Title: Beyond Log-Concavity: Sampling Challenges and Advances in Multimodal and Heavy-Tail Distributions

Abstract: 

Sampling from non-log-concave distributions poses significant challenges in a variety of fields, from Bayesian inference to computational physics and machine learning. Unlike log-concave distributions, which offer theoretical guarantees for efficient sampling, non-log-concave distributions often feature complex landscapes, including multimodality and heavy tails, that hinder standard algorithms from exploring the state space effectively. In this talk, I will discuss key obstacles and recent advances in sampling algorithms for non-log-concave distributions. First, I will explore the behavior of classical methods, such as Langevin Monte Carlo (LMC) and Proximal Sampler in the presence of multiple modes and heavy-tail behaviors, highlighting issues like metastability and slow mixing. I will then introduce techniques designed to overcome these challenges, including using denoising diffusion and novel modifications to the Gaussian noise. This presentation aims to shed light on how these innovations bridge the gap between theory and practice, offering a more nuanced understanding of sampling in complex, high-dimensional spaces. By addressing these fundamental challenges, we can deepen our insight into the behavior of advanced sampling algorithms in non-log-concave regimes.

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Colloquium: Ye He (GeorgiaTech)

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Details

Date:
10 Feb
Time:
3:30 pm – 4:30 pm

Venue

120 Hanes Hall
Hanes Hall, Chapel Hill, NC, 27599, United States

Organizer

Department of Statistics & Operations Research

Details

Date:
10 Feb
Time:
3:30 pm - 4:30 pm
Event Category:

Venue

120 Hanes Hall
Hanes Hall
Chapel Hill, NC 27599 United States
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