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作者： Bernstein, Ryan Columbia University

学位级别：Ph.D., Doctor of Philosophy

probabilistic programming is a recent advancement in probabilistic modeling whereby we can express a model as a program with little concern for the details of probabilistic inference. probabilistic programming thereby provides a clean and powerful abstraction to its users, letting even non-experts develop clear and concise models that can leverage state-of-the-art computational inference algorithms. This model-as-program representation also presents a unique opportunity: we can apply methods from the study of programming languages directly onto probabilistic models. By developing techniques to analyze, transform, or extend the capabilities of probabilistic programs, we can immediately improve the workflow of probabilistic modeling and benefit all of its applications throughout science and industry. The aim of this dissertation is to support an ideal probabilistic modeling workflow by addressing two limitations of probabilistic programming: that a program can only represent one model, and that the structure of the model that it represents is often opaque to users and to the compiler. In particular, I make the following primary contributions: (1) I introduce Multi-Model probabilistic programming: an extension of probabilistic programming whereby a program can represent a network of interrelated models. This new representation allows users to construct and leverage spaces of models in the same way that probabilistic programs do for individual models. Multi-Model probabilistic programming lets us visualize and navigate solution spaces, track and document model development paths, and audit modeler degrees of freedom to mitigate issues like p-hacking. It also provides an efficient computational foundation for the automation of model-space applications like model search, sensitivity analysis, and ensemble methods. I give a formal language specification and semantics for Multi-Model probabilistic programming built on the Stan language, I provide algorithms for the fundament

关键词： Artificial intelligence Model building probabilistic modeling probabilistic programming programming languages Statistical modeling

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JAX Based Parallel Inference for Reactive probabilistic programming 2022

JAX Based Parallel Inference for Reactive Probabilistic Prog...

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23rd International Conference on Languages, Compilers, and Tools for Embedded System (LCTES)

作者： Baudart, Guillaume Mandel, Louis Tekin, Reyyan PSL Univ DI ENS Ecole Normale Super CNRSInria Paris France IBM Res Armonk NY USA

ISBN: (纸本)9781450392662

ProbZelus is a synchronous probabilistic language for the design of reactive probabilistic models in interaction with an environment. Reactive inference methods continuously learn distributions over the unobserved parameters of the model from statistical observations. Unfortunately, this inference problem is in general intractable. Monte Carlo inference techniques thus rely on many independent executions to compute accurate approximations. These methods are expensive but can be parallelized. We propose to use JAX to parallelize ProbZelus reactive inference engine. JAX is a recent library to compile Python code which can then be executed on massively parallel architectures such as GPUs or TPUs. In this paper, we describe a new reactive inference engine implemented in JAX and the new associated JAX backend for ProbZelus. We show on existing benchmarks that our new parallel implementation outperforms the original sequential implementation for a high number of particles.

关键词： probabilistic programming Reactive programming Streaming Inference Parallel Computing Compilation

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Conditioning in probabilistic programming

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ACM TRANSACTIONS ON programming LANGUAGES AND SYSTEMS 2018年第1期40卷 4-4页

作者： Olmedo, Federico Gretz, Friedrich Jansen, Nils Kaminski, Benjamin Lucien Katoen, Joost-Pieter Mciver, Annabelle Univ Chile Dept Comp Sci Santiago Chile Bosch Corp Res Gerlingen Germany Radboud Univ Nijmegen Nijmegen Netherlands Rhein Westfal TH Aachen Ahornstr 55 D-52074 Aachen Germany Macquarie Univ Dept Comp Sydney NSW 2109 Australia Robert Bosch GmbH D-70465 Stuttgart Germany Univ Nijmegen Fac Sci Postbus 9010 NL-6500 GL Nijmegen Netherlands

This article investigates the semantic intricacies of conditioning, a main feature in probabilistic programming. Our study is based on an extension of the imperative probabilistic guarded command language pGCL with conditioning. We provide a weakest precondition (wp) semantics and an operational semantics. To deal with possibly diverging program behavior, we consider liberal preconditions. We show that diverging program behavior plays a key role when defining conditioning. We establish that weakest preconditions coincide with conditional expected rewards in Markov chains-the operational semantics-and that the wp-semantics conservatively extends the existing semantics of pGCL (without conditioning). An extension of these results with nondeterminism turns out to be problematic: although an operational semantics using Markov decision processes is rather straightforward, we show that providing an inductive wp-semantics in this setting is impossible. Finally, we present two program transformations that eliminate conditioning from any program. The first transformation hoists conditioning while updating the probabilistic choices in the program, while the second transformation replaces conditioning-in the same vein as rejection sampling-by a program with loops. In addition, we present a last program transformation that replaces an independent identically distributed loop with conditioning.

关键词： probabilistic programming conditioning weakest pre-condition semantics operational semantics

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Synthetic topology in Homotopy Type Theory for probabilistic programming

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MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE 2021年

作者： Bidlingmaier, Martin E. Faissole, Florian Spitters, Bas Aarhus Univ Dept Comp Sci Aarhus Denmark Univ Paris Saclay INRIA LRI Gif Sur Yvette France

The ALEA Coq library formalizes measure theory based on a variant of the Giry monad on the category of sets. This enables the interpretation of a probabilistic programming language with primitives for sampling from discrete distributions. However, continuous distributions have to be discretized because the corresponding measures cannot be defined on all subsets of their carriers. This paper proposes the use of synthetic topology to model continuous distributions for probabilistic computations in type theory. We study the initial sigma-frame and the corresponding induced topology on arbitrary sets. Based on these intrinsic topologies, we define valuations and lower integrals on sets and prove versions of the Riesz and Fubini theorems. We then show how the Lebesgue valuation, and hence continuous distributions, can be constructed.

关键词： probabilistic programming categorical semantics homotopy type theory topology

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PyMC: a modern, and comprehensive probabilistic programming framework in Python

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PEERJ COMPUTER SCIENCE 2023年 9卷 e1516-e1516页

作者： Abril-Pla, Oriol Andreani, Virgile Carroll, Colin Dong, Larry Fonnesbeck, Christopher J. Kochurov, Maxim Kumar, Ravin Lao, Junpeng Luhmann, Christian C. Martin, Osvaldo A. Osthege, Michael Vieira, Ricardo Wiecki, Thomas Zinkov, Robert ArviZ Devs Barcelona Spain Boston Univ Biomed Engn Dept Boston MA USA Boston Univ Biol Design Ctr Boston MA USA Google Cambridge MA USA Univ Toronto Dalla Lana Sch Publ Hlth Toronto ON Canada Hosp Sick Children Child Hlth Evaluat Sci Toronto ON Canada Philadelphia Phillies Baseball Operat Res & Dev Philadelphia PA 19148 USA PyMC Labs Berlin Germany Google Mountain View CA USA Google Zurich Switzerland SUNY Stony Brook Dept Psychol Stony Brook NY USA SUNY Stony Brook Inst Adv Computat Sci Stony Brook NY USA Univ Nacl San Luis IMASL CONICET San Luis Argentina Forschungszentrum Julich Julich Germany Univ Oxford Oxford England

PyMC is a probabilistic programming library for Python that provides tools for constructing and fitting Bayesian models. It offers an intuitive, readable syntax that is close to the natural syntax statisticians use to describe models. PyMC leverages the symbolic computation library PyTensor, allowing it to be compiled into a variety of computational backends, such as C, JAX, and Numba, which in turn offer access to different computational architectures including CPU, GPU, and TPU. Being a general modeling framework, PyMC supports a variety of models including generalized hierarchical linear regression and classification, time series, ordinary differential equations (ODEs), and non-parametric models such as Gaussian processes (GPs). We demonstrate PyMC's versatility and ease of use with examples spanning a range of common statistical models. Additionally, we discuss the positive role of PyMC in the development of the open-source ecosystem for probabilistic programming.

关键词： Bayesian statistics probabilistic programming Python Markov chain Monte Carlo Statistical modeling

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Fabular: Regression Formulas as probabilistic programming

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ACM SIGPLAN NOTICES 2016年第1期51卷 271-283页

作者： Borgstrom, Johannes Gordon, Andrew D. Ouyang, Long Russo, Claudio Scibior, Adam Szymczak, Marcin Uppsala Univ S-75105 Uppsala Sweden Microsoft Res Bangalore Karnataka India Univ Edinburgh Edinburgh EH8 9YL Midlothian Scotland Stanford Univ Stanford CA 94305 USA Univ Cambridge Cambridge CB2 1TN England MPI Tubingen Tubingen Germany

Regression formulas are a domain-specific language adopted by several R packages for describing an important and useful class of statistical models: hierarchical linear regressions. Formulas are succinct, expressive, and clearly popular, so are they a useful addition to probabilistic programming languages? And what do they mean? We propose a core calculus of hierarchical linear regression, in which regression coefficients are themselves defined by nested regressions (unlike in R). We explain how our calculus captures the essence of the formula DSL found in R. We describe the design and implementation of Fabular, a version of the Tabular schema-driven probabilistic programming language, enriched with formulas based on our regression calculus. To the best of our knowledge, this is the first formal description of the core ideas of R's formula notation, the first development of a calculus of regression formulas, and the first demonstration of the benefits of composing regression formulas and latent variables in a probabilistic programming language.

关键词： Bayesian inference linear regression probabilistic programming relational data hierarchical models

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Declarative probabilistic programming with Datalog

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ACM TRANSACTIONS ON DATABASE SYSTEMS 2017年第4期42卷 22-22页

作者： Barany, Vince Ten Cate, Balder Kimelfeld, Benny Olteanu, Dan Vagena, Zografoula LogicBlox Inc Atlanta GA 30309 USA Technion Israel Inst Technol Fac Comp Sci Taub 703 IL-32000 Haifa Israel Univ Oxford Wolfson BldgPk Rd Oxford OX1 3QD England Google Inc 1600 Amphitheatre Pkwy Mountain View CA 94043 USA Infor Inc 1349 West Peachtree St Atlanta GA 30309 USA

probabilistic programming languages are used for developing statistical models. They typically consist of two components: a specification of a stochastic process (the prior) and a specification of observations that restrict the probability space to a conditional subspace (the posterior). Use cases of such formalisms include the development of algorithms in machine learning and artificial intelligence. In this article, we establish a probabilistic-programming extension of Datalog that, on the one hand, allows for defining a rich family of statistical models, and on the other hand retains the fundamental properties of declarativity. Our proposed extension provides mechanisms to include common numerical probability functions;in particular, conclusions of rules may contain values drawn from such functions. The semantics of a program is a probability distribution over the possible outcomes of the input database with respect to the program. Observations are naturally incorporated by means of integrity constraints over the extensional and intensional relations. The resulting semantics is robust under different chases and invariant to rewritings that preserve logical equivalence.

关键词： Chase Datalog declarative probability measure space probabilistic programming

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A Lambda-Calculus Foundation for Universal probabilistic programming

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ACM SIGPLAN NOTICES 2016年第9期51卷 33-46页

作者： Borgstrom, Johannes Dal Lago, Ugo Gordon, Andrew D. Szymczak, Marcin Uppsala Univ Uppsala Sweden Univ Bologna I-40126 Bologna Italy INRIA Rocquencourt France Microsoft Res Cambridge England Univ Edinburgh Edinburgh EH8 9YL Midlothian Scotland

We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, and both hard and soft constraints, as a foundation for universal probabilistic programming languages such as CHURCH, ANGLICAN, and VENTURE. Our first contribution is to adapt the classic operational semantics of lambda-calculus to a continuous setting via creating a measure space on terms and defining step-indexed approximations. We prove equivalence of big-step and small-step formulations of this distribution-based semantics. To move closer to inference techniques, we also define the sampling-based semantics of a term as a function from a trace of random samples to a value. We show that the distribution induced by integration over the space of traces equals the distribution-based semantics. Our second contribution is to formalize the implementation technique of trace Markov chain Monte Carlo (MCMC) for our calculus and to show its correctness. A key step is defining sufficient conditions for the distribution induced by trace MCMC to converge to the distribution-based semantics. To the best of our knowledge, this is the first rigorous correctness proof for trace MCMC for a higher-order functional language, or for a language with soft constraints.

关键词： probabilistic programming Lambda-calculus MCMC Machine Learning Operational Semantics

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Replicated Computational Results (RCR) Report for "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 4-4页

作者： Parker, David Univ Birmingham Sch Comp Sci Birmingham B15 2TT W Midlands England

"ProPPA: probabilistic programming for Stochastic Dynamical Systems," by Georgoulas, Hillston, and Sanguinetti, introduces the ProPPA formalism, which brings together ideas from stochastic process algebras with those from the paradigm of probabilistic programming. The article formally defines the ProPPA language and its semantics and presents a tool-set, along with results from illustrative examples. This replicated computational results report installs and runs the tool-set and repeats the simulation-based results from the article, finding that the published results are repeatable.

关键词： RCR report process algebra probabilistic programming

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Practical probabilistic programming with Monads

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ACM SIGPLAN NOTICES 2015年第12期50卷 165-176页

作者： Scibior, Adam Ghahramani, Zoubin Gordon, Andrew D. Univ Cambridge Cambridge CB2 1TN England Microsoft Res Redmond WA USA Univ Edinburgh Edinburgh EH8 9YL Midlothian Scotland

The machine learning community has recently shown a lot of interest in practical probabilistic programming systems that target the problem of Bayesian inference. Such systems come in different forms, but they all express probabilistic models as computational processes using syntax resembling programming languages. In the functional programming community monads are known to offer a convenient and elegant abstraction for programming with probability distributions, but their use is often limited to very simple inference problems. We show that it is possible to use the monad abstraction to construct probabilistic models for machine learning, while still offering good performance of inference in challenging models. We use a GADT as an underlying representation of a probability distribution and apply Sequential Monte Carlo-based methods to achieve efficient inference. We define a formal semantics via measure theory. We demonstrate a clean and elegant implementation that achieves performance comparable with Anglican, a stateof- the-art probabilistic programming system.

关键词： Haskell probabilistic programming Bayesian statistics monads Monte Carlo

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