Relatore: Bob Carpenter, Center for Computational Mathematics, Flatiron Institute, New York

Abstract:  I will present a novel and flexible framework for localized tuning of Metropolis samplers, including Hamiltonian Monte Carlo (HMC).  In the Gibbs self tuning (GIST) framework, an algorithm's tuning parameters are Gibbs sampled each iteration conditioned on the current position and momentum.  For adaptively sampling path lengths, I will show that randomized integration time Hamiltonian Monte Carlo, the no-U-turn sampler, and the apogee-to-apogee path sampler all fit within this unified framework as special cases.  I'll provide two new examples.

One is a multinomial form of randomized bidirectional HMC with a 100% acceptance rate.  The second is a much simpler alternative to the no-U-turn sampler for locally adapting path lengths.  In all of these samplers, correctness depends on simulating the Hamiltonian dynamics forward and backward randomly in time.  The key to making local tuning practical is randomization, which as Andrew Gelman likes to say, "greases the wheels of commerce."  I will conclude with a discussion of the opportunity this framework presents for adapting HMC's step size and mass matrix.

Joint work with Nawaf Bou-Rabee (Rutgers), Milo Marsden (Stanford), Edward Roualdes (Cal State), Chirag Modi (Flatiron), and Gilad Turok

(Flatiron)

BIO:

Bob Carpenter is a research scientist at Flatiron Institute's Center for Computational Mathematics.  He works on probabilistic programming languages, statistical inference algorithms, and applied statistics, primarily within the Stan community (https://mc-stan.org).  Before moving into statistics, Bob worked on theoretical linguistics, logic programming, natural language processing, and speech recognition, both in industry and academia.