Theory Seminar - Amit Rajaraman

— 11:30am

Location:
In Person - Gates Hillman 8102

Speaker:
AMIT RAJARAMAN , Ph.D. Student, Theory Group , Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology
https://amitrajaraman.github.io/

Weak Poincaré Inequalities and Mixing from Non-Worst-Case Initializations

There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as Poincaré inequalities. In many situations, Markov chains fail to mix rapidly from a worst-case initialization, yet are expected to approximately sample from a random initialization. Under such conditions, a Poincaré inequality does not hold, necessitating new tools to prove sampling guarantees. 

We develop a framework to analyze such initializations, based on establishing so-called "weak Poincaré inequalities." As an application, we prove that "simulated annealing" samples from the Gibbs measure of a spherical spin glass for inverse temperatures up to a natural threshold, matching recent algorithms based on algorithmic stochastic localization. In this talk, we will focus on an application of our techniques to sampling from mixtures of log-concave distributions using data-based initializations. 

Based on joint work with Brice Huang (MIT), Sidhanth Mohanty (MIT), and David X Wu (Berkeley)  

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