82 citations · 204 across the 14 of their papers we have counts for
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Mixing on Columns of the Transvection Walk
Natesh Pillai, Aaron Smith
In Diaconis and Saloff-Coste (1996), the authors introduced the simple ``transvection" walk on : at each step, choose two distinct rows and add one to t…
Kac's walk on rotation matrices mixes in steps
Natesh S. Pillai, Aaron Smith
Kac's walk on the rotation group, introduced by Hastings in 1970, is an important high-dimensional Markov chain with applications in statistical physics, statistics, cryptography,…
Perturbation Analysis of Markov Chain Monte Carlo for Graphical Models
Na Lin, Yuanyuan Liu, Aaron Smith
The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributio…
Does Hamiltonian Monte Carlo mix faster than a random walk on multimodal densities?
Oren Mangoubi, Natesh S. Pillai, Aaron Smith
Hamiltonian Monte Carlo (HMC) is a very popular and generic collection of Markov chain Monte Carlo (MCMC) algorithms. One explanation for the popularity of HMC algorithms is their…
Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions
Oren Mangoubi, Aaron Smith
We obtain several quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm for a strongly log-concave target distribution on …
Rapid Mixing of Geodesic Walks on Manifolds with Positive Curvature
Oren Mangoubi, Aaron Smith
We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold , which we call the . We prove that the mixing…