A probabilistic language based upon sampling functions

As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages that treat probability distributions as primitive datatypes. Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power. In this paper, we present a probabilistic language, called λο, which uniformly supports all kinds of probability distributions -- discrete distributions, continuous distributions, and even those belonging to neither group. Its mathematical basis is sampling functions, i.e., mappings from the unit interval (0.0,1.0] to probability domains.We also briefly describe the implementation of λο as an extension of Objective CAML and demonstrate its practicality with three applications in robotics: robot localization, people tracking, and robotic mapping. All experiments have been carried out with real robots.

[1]  John T. Gill,et al.  Computational complexity of probabilistic Turing machines , 1974, STOC '74.

[2]  N. Saheb-Djahromi,et al.  Probabilistic LCF , 1978, International Symposium on Mathematical Foundations of Computer Science.

[3]  Dexter Kozen,et al.  Semantics of probabilistic programs , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[4]  Linus Schrage,et al.  A guide to simulation , 1983 .

[5]  Paul Bratley,et al.  A guide to simulation , 1983 .

[6]  Max Henrion,et al.  Propagating uncertainty in bayesian networks by probabilistic logic sampling , 1986, UAI.

[7]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[8]  Paul Bratley,et al.  A guide to simulation (2nd ed.) , 1986 .

[9]  W. Rudin.  Real and complex analysis, 3rd ed. , 1987 .

[10]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[11]  Eugenio Moggi,et al.  Computational lambda-calculus and monads , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[12]  Claire Jones,et al.  Probabilistic non-determinism , 1990 .

[13]  Paul Bratley,et al.  Guide to Simulation, 2nd Edition.@@@Simulation Methodology for Statisticians, Operations Analysis, and Engineers. , 1990 .

[14]  Eugenio Moggi,et al.  Notions of Computation and Monads , 1991, Inf. Comput..

[15]  Simon L. Peyton Jones,et al.  Imperative functional programming , 1993, POPL '93.

[16]  Eugene Charniak,et al.  Statistical language learning , 1997 .

[17]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[18]  Simon L. Peyton Jones,et al.  State in Haskell , 1995, LISP Symb. Comput..

[19]  Rajeev Motwani,et al.  Randomized algorithms , 1996, CSUR.

[20]  P. Martin-Löf.  On the meanings of the logical constants and the justi cations of the logical laws , 1996 .

[21]  Philip Wadler,et al.  A reflection on call-by-value , 1997, TOPL.

[22]  Frederick Jelinek,et al.  Statistical methods for speech recognition , 1997 .

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

[24]  David J. C. Mackay,et al.  Introduction to Monte Carlo Methods , 1998, Learning in Graphical Models.

[25]  W. Burgard,et al.  Markov Localization for Mobile Robots in Dynamic Environments , 1999, J. Artif. Intell. Res..

[26]  Radha Jagadeesan,et al.  Stochastic processes as concurrent constraint programs , 1999, POPL '99.

[27]  Russ Bubley,et al.  Randomized algorithms , 2018, CSUR.

[28]  Sebastian Thrun,et al.  Probabilistic Algorithms in Robotics , 2000, AI Mag..

[29]  Sebastian Thrun,et al.  Towards programming tools for robots that integrate probabilistic computation and learning , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[30]  Xavier Leroy,et al.  A modular module system , 2000, J. Funct. Program..

[31]  Frank Pfenning,et al.  A judgmental reconstruction of modal logic , 2001, Mathematical Structures in Computer Science.

[32]  Avi Pfeffer,et al.  IBAL: A Probabilistic Rational Programming Language , 2001, IJCAI.

[33]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[34]  George F. Luger,et al.  Toward General Analysis of Recursive Probability Models , 2001, UAI.

[35]  Norman Ramsey,et al.  Stochastic lambda calculus and monads of probability distributions , 2002, POPL '02.

[36]  William Whittaker,et al.  Conditional particle filters for simultaneous mobile robot localization and people-tracking , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[37]  Sebastian Thrun,et al.  FastSLAM: a factored solution to the simultaneous localization and mapping problem , 2002, AAAI/IAAI.

[38]  Torben Æ. Mogensen.  Roll : A Language for Specifying Die-Rolls , 2003, PADL.

[39]  Sungwoo Park,et al.  A calculus for probabilistic languages , 2003, TLDI '03.

[40]  Sebastian Thrun,et al.  FastSLAM 2.0: an improved particle filtering algorithm for simultaneous localization and mapping that provably converges , 2003, IJCAI 2003.

[41]  Sebastian Thrun,et al.  Robotic mapping: a survey , 2003 .

[42]  J. L. Roux.  An Introduction to the Kalman Filter , 2003 .

[43]  Michael Isard,et al.  CONDENSATION—Conditional Density Propagation for Visual Tracking , 1998, International Journal of Computer Vision.

[44]  A probabilistic language based upon sampling functions , 2005, POPL.

[45]  Simon Peyton Jones,et al.  Tackling the Awkward Squad: monadic input/output, concurrency, exceptions, and foreign-language calls in Haskell , 2005 .

[46]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.