Geometry on Demand: An Efficient Sampling Algorithm for High-Dimensional Problems

• Activity Number: 89
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 8:30 PM to 9:15 PM
• Sponsor: Korean International Statistical Society
• Author(s): Shiwei Lan* and Babak Shahbaba
• Companies: University of Warwick and UC Irvine
• Keywords: Markov Chain Monte Carlo ; Hamiltonian Monte Carlo ; Riemannian manifold

Abstract

Hamiltonian Monte Carlo (HMC) is a Metropolis algorithm that can generate distant proposals (guided by Hamiltonian dynamics) with high probability of acceptance. It suppresses the random walk behavior by using the gradient information. Riemannian HMC improves standard HMC by using Fisher information to adapt to the local geometry of parameter space. Although, using geometric information could help sampling algorithms to explore parameter space more efficiently, its computational overhead is not always justified. Here, we propose a new algorithm that uses geometry on demand. At each state of Markov chain, it calculates and uses Fisher information only when the resulting improvement in sampling efficiency is deemed to overwhelm its computational overhead. Several experiments are presented to demonstrate the advantages of our algorithm.