tfp.mcmc: Modern Markov Chain Monte Carlo Tools Built for Modern Hardware

Markov chain Monte Carlo (MCMC) is widely regarded as one of the most important algorithms of the 20th century. Its guarantees of asymptotic convergence, stability, and estimator-variance bounds using only unnormalized probability functions make it indispensable to probabilistic programming. In this paper, we introduce the TensorFlow Probability MCMC toolkit, and discuss some of the considerations that motivated its design.

[1]  Dustin Tran,et al.  TensorFlow Distributions , 2017, ArXiv.

[2]  Jiqiang Guo,et al.  Stan: A Probabilistic Programming Language. , 2017, Journal of statistical software.

[3]  Noah D. Goodman,et al.  Pyro: Deep Universal Probabilistic Programming , 2018, J. Mach. Learn. Res..

[4]  Nicolai Schipper Jespersen,et al.  An Introduction to Markov Chain Monte Carlo , 2010 .

[5]  Martín Abadi,et al.  TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems , 2016, ArXiv.

[6]  Daniel Foreman-Mackey,et al.  emcee: The MCMC Hammer , 2012, 1202.3665.

[7]  Aki Vehtari,et al.  ELFI: Engine for Likelihood Free Inference , 2016, J. Mach. Learn. Res..

[8]  Andrew Gelman,et al.  The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo , 2011, J. Mach. Learn. Res..

[9]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[10]  Radford M. Neal.  MCMC Using Hamiltonian Dynamics , 2011, 1206.1901.

[11]  John Salvatier,et al.  Probabilistic programming in Python using PyMC3 , 2016, PeerJ Comput. Sci..

[12]  Joshua V. Dillon,et al.  NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport , 2019, 1903.03704.

[13]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[14]  Cajo J. F. ter Braak,et al.  A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces , 2006, Stat. Comput..

[15]  Christian P. Robert,et al.  Monte Carlo Statistical Methods (Springer Texts in Statistics) , 2005 .

[16]  Andrew Gelman,et al.  Handbook of Markov Chain Monte Carlo , 2011 .

[17]  Radford M. Neal.  Probabilistic Inference Using Markov Chain Monte Carlo Methods , 2011 .