May 18, 2022, SES 138
2:30-3:00: Welcome, discussion
3:00-3:40: Entropic independence
Vishesh Jain (Stanford)
I will introduce entropic independence, which is an entropic analog of the recently established notion of spectral independence, and discuss how it may be used to obtain asymptotically sharp results on the mixing times of certain `local' random walks such as the Glauber dynamics for the Ising model or the hard-core model in the tree-uniquess regime. Based on joint works with Nima Anari, Frederic Koehler, Huy Tuan Pham, and Thuy-Duong Vuong.
3:45-4:25: On the Robustness to Misspecification of α-Posteriors and Their Variational Approximations
Cynthia Rush (Columbia)
Variational inference (VI) is a machine learning technique that approximates difficult-to-compute probability densities by using optimization. While VI has been used in numerous applications, it is particularly useful in Bayesian statistics where one wishes to perform statistical inference about unknown parameters through calculations on a posterior density. In this talk, I will review the core concepts of VI and introduce some new ideas about VI and robustness to model misspecification. In particular, we will study α-posteriors, which distort standard posterior inference by downweighting the likelihood, and their variational approximations. We will see that such distortions, if tuned appropriately, can outperform standard posterior inference when there is potential parametric model misspecification. This is joint work with Marco Avella Medina, José Luis Montiel Olea, and Amilcar Velez.
4:30-5:10: Phase Transitions for Random Forests
Tyler Helmuth (Durham)
Bond percolation has been intensively studied for several decades in probability and combinatorics. Given a graph, ‘open’ each edge independently with probability p, and leave them ‘closed’ with probability 1-p. What is the geometry of the subgraph of open edges? A basic question is whether or not the subgraph of open edges has a ‘giant’ connected component: one that contains a positive fraction of the vertices of the graph. In this talk I’ll discuss a problem with a similar flavour. The arboreal gas is the probability law that arises when conditioning bond percolation on the event that the subgraph of open edges is a forest. What is the geometry of such a forest? This question arises naturally in the context of the q-state Potts model from statistical mechanics, and the singular conditioning of bond percolation to be a forest leads to some surprising phenomena. I’ll describe what is known and conjectured. Based on joint work with R. Bauerschmidt, N. Crawford, A. Swan.