机器学习与数据科学博士生系列论坛(第八十二期)—— Lower Bounds for Log-concave Sampling
Holder: Yuchen Xin(Peking University)
Time:2024-12-26 16:00-17:00
Location:Tencent Conference 568-7810-5726
Abstract:
In recent years, there has been great progress in developing faster algorithms for log-concave sampling. It's natural to ask whether the algorithmic upper bounds are tight. Thus, it's necessary to establish query complexity lower bounds for sampling.
In this talk, we will introduce some results on query lower bounds for log-concave sampling, based on a recent work by Chewi, Pont, Li, Lu, Narayanan[2023]. We will also introduce a lower bound for sampling algorithms which simulate underdamped Langevin dynamics, based on a work by Cao, Lu, Wang[2019].In this talk we will introduce the concept of "intrinsic freeness", which provides sharper bounds than the traditional noncommutative Khintchine inequality, especially in cases where the latter is suboptimal. We also show how to use Gaussian interpolation to solve these problems, and finally illustrate the practical significance of this theorem through various examples.
About the Speaker:
论坛每次邀请一位博士生就某个前沿课题做较为系统深入的介绍,主题包括但不限于机器学习、高维统计学、运筹优化和理论计算机科学。
Your participation is warmly welcomed!

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