R2: An Efficient MCMC Sampler for Probabilistic Programs

We present a new Markov Chain Monte Carlo (MCMC) sampling algorithm for probabilistic programs. Our approach and tool, called R2, has the unique feature of employing program analysis in order to improve the efficiency of MCMC sampling. Given an input program P, R2 propagates observations in P backwards to obtain a semantically equivalent program P′ in which every probabilistic assignment is immediately followed by an observe statement. Inference is performed by a suitably modified version of the Metropolis-Hastings algorithm that exploits the structure of the program P′. This has the overall effect of preventing rejections due to program executions that fail to satisfy observations in P. We formalize the semantics of probabilistic programs and rigorously prove the correctness of R2. We also empirically demonstrate the effectiveness of R2--in particular, we show that R2 is able to produce results of similar quality as the CHURCH and STAN probabilistic programming tools with much shorter execution time.

[1]  A. Macdonald.  A Statistician , 1921 .

[2]  Edsger W. Dijkstra,et al.  A Discipline of Programming , 1976 .

[3]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[4]  Walter R. Gilks,et al.  A Language and Program for Complex Bayesian Modelling , 1994 .

[5]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[6]  David A. McAllester,et al.  Effective Bayesian Inference for Stochastic Programs , 1997, AAAI/IAAI.

[7]  Avi Pfeffer,et al.  The Design and Implementation of IBAL: A General-Purpose Probabilistic Language , 2005 .

[8]  Stuart J. Russell,et al.  General-Purpose MCMC Inference over Relational Structures , 2006, UAI.

[9]  Tom Minka,et al.  TrueSkillTM: A Bayesian Skill Rating System , 2006, NIPS.

[10]  Matthew Richardson,et al.  The Alchemy System for Statistical Relational AI: User Manual , 2007 .

[11]  Luc De Raedt,et al.  ProbLog: A Probabilistic Prolog and its Application in Link Discovery , 2007, IJCAI.

[12]  Avi Pfeffer,et al.  A General Importance Sampling Algorithm for Probabilistic Programs , 2007 .

[13]  Thomas Hofmann,et al.  TrueSkill™: A Bayesian Skill Rating System , 2007 .

[14]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.

[15]  Joshua B. Tenenbaum,et al.  Church: a language for generative models , 2008, UAI.

[16]  Chung-chieh Shan,et al.  Monolingual Probabilistic Programming Using Generalized Coroutines , 2009, UAI.

[17]  Nir Friedman,et al.  Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning , 2009 .

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

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

[20]  Noah D. Goodman,et al.  Nonstandard Interpretations of Probabilistic Programs for Efficient Inference , 2011, NIPS.

[21]  Noah D. Goodman,et al.  Lightweight Implementations of Probabilistic Programming Languages Via Transformational Compilation , 2011, AISTATS.

[22]  Luc De Raedt,et al.  MCMC Estimation of Conditional Probabilities in Probabilistic Programming Languages , 2013, ECSQARU.

[23]  Sriram K. Rajamani,et al.  Efficiently Sampling Probabilistic Programs via Program Analysis , 2013, AISTATS.

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