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Implementing a Library for probabilistic programming Using Non-strict Non-determinism

THEORY AND PRACTICE OF LOGIC programming 2020年第1期20卷 147-175页

作者： Dylus, Sandra Christiansen, Jan Teegen, Finn Univ Kiel Kiel Germany Flensburg Univ Appl Sci Flensburg Germany

This paper presents PFLP, a library for probabilistic programming in the functional logic programming language Curry. It demonstrates how the concepts of a functional logic programming language support the implementation of a library for probabilistic programming. In fact, the paradigms of functional logic and probabilistic programming are closely connected. That is, language characteristics from one area exist in the other and vice versa. For example, the concepts of non-deterministic choice and call-time choice as known from functional logic programming are related to and coincide with stochastic memoization and probabilistic choice in probabilistic programming, respectively. We will further see that an implementation based on the concepts of functional logic programming can have benefits with respect to performance compared to a standard list-based implementation and can even compete with full-blown probabilistic programming languages, which we illustrate by several benchmarks.

关键词： probabilistic programming functional logic programming non-determinism laziness call-time choice

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ProPPA: probabilistic programming for Stochastic Dynamical Systems

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ACM TRANSACTIONS ON MODELING AND COMPUTER SIMULATION 2018年第1期28卷 1–23页

作者： Georgoulas, Anastasis Hillston, Jane Sanguinetti, Guido UCL Res IT Serv Res Software Dev Grp 1 Eversholt St London NW1 2DN England Univ Edinburgh Sch Informat 10 Crichton St Edinburgh EH8 9AB Midlothian Scotland

Formal languages like process algebras have been shown to be effective tools in modelling a wide range of dynamic systems, providing a high-level description that is readily transformed into an executable model. However, their application is sometimes hampered because the quantitative details of many real-world systems of interest are not fully known. In contrast, in machine learning, there has been work to develop probabilistic programming languages, which provide system descriptions that incorporate uncertainty and leverage advanced statistical techniques to infer unknown parameters from observed data. Unfortunately, current probabilistic programming languages are typically too low-level to be suitable for complex modelling. In this article, we present a probabilistic programming Process Algebra (ProPPA), the first instance of the probabilistic programming paradigm being applied to a high-level, formal language, and its supporting tool suite. We explain the semantics of the language in terms of a quantitative generalisation of Constraint Markov Chains and describe the implementation of the language, discussing in some detail the different inference algorithms available and their domain of applicability. We conclude by illustrating the use of the language on simple but non-trivial case studies: here, ProPPA is shown to combine the elegance and simplicity of high-level formal modelling languages with an effective way of incorporating data, making it a promising tool for modelling studies.

关键词： Process algebra stochastic modelling probabilistic programming parameter estimation

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Automated learning with a probabilistic programming language: Birch

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ANNUAL REVIEWS IN CONTROL 2018年 46卷 29-43页

作者： Murray, Lawrence M. Schon, Thomas B. Uppsala Univ Dept Informat Technol SE-751 Uppsala 05 Sweden

This work offers a broad perspective on probabilistic modeling and inference in light of recent advances in probabilistic programming, in which models are formally expressed in Turing-complete programming languages. We consider a typical workflow and how probabilistic programming languages can help to automate this workflow, especially in the matching of models with inference methods. We focus on two properties of a model that are critical in this matching: its structure the conditional dependencies between random variables and its form the precise mathematical definition of those dependencies. While the structure and form of a probabilistic model are often fixed a priori, it is a curiosity of probabilistic programming that they need not be, and may instead vary according to random choices made during program execution. We introduce a formal description of models expressed as programs, and discuss some of the ways in which probabilistic programming languages can reveal the structure and form of these, in order to tailor inference methods. We demonstrate the ideas with a new probabilistic programming language called Birch, with a multiple object tracking example. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： probabilistic programming System identification Machine learning Monte Carlo Multi object tracking

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Pyro: Deep Universal probabilistic programming

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JOURNAL OF MACHINE LEARNING RESEARCH 2019年第1期20卷 973-978页

作者： Bingham, Eli Chen, Jonathan P. Jankowiak, Martin Obermeyer, Fritz Pradhan, Neeraj Karaletsos, Theofanis Singh, Rohit Szerlip, Paul Horsfall, Paul Goodman, Noah D. Uber Technol Inc Uber AI Labs 555 Market St San Francisco CA 94103 USA Uber AI Labs 555 Market St San Francisco CA 94103 USA Stanford Univ Stanford CA 94305 USA

Pyro is a probabilistic programming language built on Python as a platform for developing advanced probabilistic models in AI research. To scale to large data sets and high-dimensional models, Pyro uses stochastic variational inference algorithms and probability distributions built on top of PyTorch, a modern GPU-accelerated deep learning framework. To accommodate complex or model-specific algorithmic behavior, Pyro leverages Poutine, a library of composable building blocks for modifying the behavior of probabilistic programs.

关键词： probabilistic programming graphical models approximate Bayesian inference generative models deep learning

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Semi-symbolic Inference for Efficient Streaming probabilistic programming

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2022年第OOPSLA期6卷 1668–1696页

作者： Atkinson, Eric Yuan, Charles Baudart, Guillaume Mandel, Louis Carbin, Michael MIT Cambridge MA 02139 USA PSL Univ CNRS ENS InriaDI ENS Paris France IBM Res MIT IBM Watson Lab Cambridge MA USA

A streaming probabilistic program receives a stream of observations and produces a stream of distributions that are conditioned on these observations. Efficient inference is often possible in a streaming context using Rao-Blackwellized particle filters (RBPFs), which exactly solve inference problems when possible and fall back on sampling approximations when necessary. While RBPFs can be implemented by hand to provide efficient inference, the goal of streaming probabilistic programming is to automatically generate such efficient inference implementations given input probabilistic programs. In this work, we propose semi-symbolic inference, a technique for executing probabilistic programs using a runtime inference system that automatically implements Rao-Blackwellized particle filtering. To perform exact and approximate inference together, the semi-symbolic inference system manipulates symbolic distributions to perform exact inference when possible and falls back on approximate sampling when necessary. This approach enables the system to implement the same RBPF a developer would write by hand. To ensure this, we identify closed families of distributions - such as linear-Gaussian and finite discrete models - on which the inference system guarantees exact inference. We have implemented the runtime inference system in the ProbZelus streaming probabilistic programming language. Despite an average 1.6x slowdown compared to the state of the art on existing benchmarks, our evaluation shows that speedups of 3xs87x are obtainable on a new set of challenging benchmarks we have designed to exploit closed families.

关键词： probabilistic programming streaming inference

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Note on Solving probabilistic programming Problems Involving Multi-choice Parameters

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JOURNAL OF INTERDISCIPLINARY MATHEMATICS 2015年第5期18卷 617-627页

作者： Hung, Kuo-Chen Lin, Scott Shu-Cheng Chu, Chun-Hsiao Hungkuang Univ Dept Comp Sci & Informat Management Taichung Taiwan Chungyu Inst Technol Dept Tourism & Travel Management Keelung Taiwan Aletheia Univ Dept Tourism New Taipei Taiwan

We study the probabilistic programming problems with multi-choice parameters proposed by Acharya and Biswal (2011) that was published in Opsearch. We point out that the multi-choice parameters can be simplified to avoid the complicated solution procedure proposed by Acharya and Biswal (2011). We use the same numerical example of Acharya and Biswal (2011) to demonstrate that our simplification is effective to derive better minimum.

关键词： probabilistic programming multi-choice programming non-linear programming deterministic programming

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Static Posterior Inference of Bayesian probabilistic programming via Polynomial Solving

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2024年第PLDI期8卷 1361-1386页

作者： Wang, Peixin Yang, Tengshun Fu, Hongfei Li, Guanyan Ong, C. -H. Luke Nanyang Technol Univ Singapore Singapore Chinese Acad Sci Inst Software Beijing Peoples R China Univ Chinese Acad Sci Beijing Peoples R China Shanghai Jiao Tong Univ Shanghai Peoples R China Univ Oxford Oxford England

In Bayesian probabilistic programming, a central problem is to estimate the normalised posterior distribution (NPD) of a probabilistic program with conditioning via score (a.k.a. observe) statements. Most previous approaches address this problem by Markov Chain Monte Carlo and variational inference, and therefore could not generate guaranteed outcomes within a finite time limit. Moreover, existing methods for exact inference either impose syntactic restrictions or cannot guarantee successful inference in general. In this work, we propose a novel automated approach to derive guaranteed bounds for NPD via polynomial solving. We first establish a fixed-point theorem for the wide class of score-at-end Bayesian probabilistic programs that terminate almost-surely and have a single bounded score statement at program termination. Then, we propose a multiplicative variant of Optional Stopping Theorem (OST) to address score-recursive Bayesian programs where score statements with weights greater than one could appear inside a loop. Bayesian nonparametric models, enjoying a renaissance in statistics and machine learning, can be represented by score-recursive Bayesian programs and are difficult to handle due to an integrability issue. Finally, we use polynomial solving to implement our fixed-point theorem and OST variant. To improve the accuracy of the polynomial solving, we further propose a truncation operation and the synthesis of multiple bounds over various program inputs. Our approach can handle Bayesian probabilistic programs with unbounded while loops and continuous distributions with infinite supports. Experiments over a wide range of benchmarks show that compared with the most relevant approach (Beutner et al., PLDI 2022) for guaranteed NPD analysis via recursion unrolling, our approach is more time efficient and derives comparable or even tighter NPD bounds. Furthermore, our approach can handle score-recursive programs which previous approaches could not.

关键词： probabilistic programming Bayesian inference static analysis martingales fixed-point theory posterior distributions

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Syntax and operational semantics of a probabilistic programming language with scopes

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JOURNAL OF MATHEMATICAL PSYCHOLOGY 2016年 74卷 46-57页

作者： Bruza, Peter D. QUT Sch Informat Syst GPO Box 2434 Brisbane Qld Australia

Dzhafarov and Kujala (2015) have introduced a contextual probability theory called Contextuality-by-Default (C-b-D) which is based on three principles. The first of these principles states that each random variable should be automatically labelled by all conditions under which it is recorded. The aim of this article is to relate this principle to block structured computer programming languages where variables are declared local to a construct called a "scope". Scopes are syntactic constructs which correspond to the notion of condition used by C-b-D. In this way a variable declared in two scopes can be safely overloaded meaning that they can have the same label but preserve two distinct identities without the need to label each variable in each condition as advocated by C-b-D. By means of examples, the notion of a probabilistic-program, or P-program, is introduced which is based on scopes. The semantics of P-programs will be illustrated using the well known relational database language SQL which provides an efficient and understandable operational semantics. A core issue addressed is how to construct a single probabilistic model from the various interim probability distributions returned by each syntactic scope. For this purpose, a probabilistic variant of the natural join operator of relational algebra is used to "glue" together interim distributions into a single distribution. More generally, this article attempts to connect contextuality with probabilistic programming by means of relational database theory. (C) 2016 Published by Elsevier Inc.

关键词： probabilistic programming probabilistic modelling programming language semantics Contextuality Contextuality-by-Default

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Verified Density Compilation for a probabilistic programming Language

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2023年第PLDI期7卷 615-637页

作者： Tassarotti, Joseph Tristan, Jean-Baptiste NYU New York NY USA AWS Boston MA USA

This paper presents ProbCompCert, a compiler for a subset of the Stan probabilistic programming language (PPL), in which several key compiler passes have been formally verified using the Coq proof assistant. Because of the probabilistic nature of PPLs, bugs in their compilers can be difficult to detect and fix, making verification an interesting possibility. However, proving correctness of PPL compilation requires new techniques because certain transformations performed by compilers for PPLs are quite different from other kinds of languages. This paper describes techniques for verifying such transformations and their application in ProbCompCert. In the course of verifying ProbCompCert, we found an error in the Stan language reference manual related to the semantics and implementation of a key language construct.

关键词： compilers probabilistic programming formal verification

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Paradoxes of probabilistic programming And How to Condition on Events of Measure Zero with Infinitesimal Probabilities

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2021年第POPL期5卷 1–26页

作者： Jacobs, Jules Radboud Univ Nijmegen Nijmegen Netherlands Delft Univ Technol Delft Netherlands

probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating likelihood at each observe statement, and using the likelihood to steer random choices and weigh results with inference algorithms such as importance sampling or MCMC. We argue that naive likelihood accumulation does not give desirable semantics and leads to paradoxes when an observe statement is used to condition on a measure-zero event, particularly when the observe statement is executed conditionally on random data. We show that the paradoxes disappear if we explicitly model measure-zero events as a limit of positive measure events, and that we can execute these type of probabilistic programs by accumulating infinitesimal probabilities rather than probability densities. Our extension improves probabilistic programming languages as an executable notation for probability distributions by making it more well-behaved and more expressive, by allowing the programmer to be explicit about which limit is intended when conditioning on an event of measure zero.

关键词： probabilistic programming

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