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A Unifying Approach to Product Constructions for Quantitative Temporal Inference

Proceedings of the ACM on programming Languages 2025年第1期9卷 1575-1603页

作者： Watanabe, Kazuki Junges, Sebastian Rot, Jurriaan Hasuo, Ichiro National Institute of Informatics Japan Japan Radboud University Netherlands

probabilistic programs are a powerful and convenient approach to formalising distributions over system executions. A classical verification problem for probabilistic programs is temporal inference: to compute the likelihood that the execution traces satisfy a given temporal property. This paper presents a general framework for temporal inference, which applies to a rich variety of quantitative models including those that arise in the operational semantics of probabilistic and weighted programs. The key idea underlying our framework is that in a variety of existing approaches, the main construction that enables temporal inference is that of a product between the system of interest and the temporal property. We provide a unifying mathematical definition of product constructions, enabled by the realisation that 1) both systems and temporal properties can be modelled as coalgebras and 2) product constructions are distributive laws in this context. Our categorical framework leads us to our main contribution: a sufficient condition for correctness, which is precisely what enables to use the product construction for temporal inference. We show that our framework can be instantiated to naturally recover a number of disparate approaches from the literature including, e.g., partial expected rewards in Markov reward models, resource-sensitive reachability analysis, and weighted optimization problems. Furthermore, we demonstrate a product of weighted programs and weighted temporal properties as a new instance to show the scalability of our approach. © 2025 Copyright held by the owner/author(s).

关键词： coalgebra probabilistic programming temporal inference

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NeST: The neuro-symbolic transpiler

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2025年 179卷

作者： Pfanschilling, Viktor Shindo, Hikaru Dhami, Devendra Singh Kersting, Kristian Tech Univ Darmstadt Comp Sci Dept Hsch Str 1 D-64289 Darmstadt Germany Hessian Ctr Artificial Intellifence Hessian AI Landwehrstr 50a D-64293 Darmstadt Germany German Res Ctr Artificial Intelligence DFKI Landwehrstr 50a D-64293 Darmstadt Germany Eindhoven Univ Technol Dept Math & Comp Sci Room 7-142 NL-5612 AZ Eindhoven Netherlands

Tractable probabilistic Models such as Sum-Product Networks are a powerful category of models that offer a rich choice of fast probabilistic queries. However, they are limited in the distributions they can represent, e.g., they cannot define distributions using loops or recursion. To move towards more complex distributions, we introduce a novel neurosymbolic programming language, Sum Product Loop Language (SPLL), along with the Neuro-Symbolic Transpiler (NeST). SPLL aims to build inference code most closely resembling Tractable probabilistic Models. NeST is the first neuro-symbolic transpiler-a compiler from one high-level language to another. It generates inference code from SPLL but natively supports other computing platforms, too. This way, SPLL can seamlessly interface with e.g. pretrained (neural) models in PyTorch or Julia. The result is a language that can run probabilistic inference on more generalized distributions, reason on neural network outputs, and provide gradients for training.

关键词： probabilistic programming Neuro-symbolic Large language models Tractable probabilistic models

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Reasoning about reasoning by nested conditioning: Modeling theory of mind with probabilistic programs

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COGNITIVE SYSTEMS RESEARCH 2014年第1期28卷 80-99页

作者： Stuhlmueller, A. Goodman, N. D. MIT Dept Brain & Cognit Sci Cambridge MA 02139 USA Stanford Univ Dept Psychol Stanford CA 94305 USA

A wide range of human reasoning patterns can be explained as conditioning in probabilistic models;however, conditioning has traditionally been viewed as an operation applied to such models, not represented in such models. We describe how probabilistic programs can explicitly represent conditioning as part of a model. This enables us to describe reasoning about others' reasoning using nested conditioning. Much of human reasoning is about the beliefs, desires, and intentions of other people;we use probabilistic programs to formalize these inferences in a way that captures the flexibility and inherent uncertainty of reasoning about other agents. We express examples from game theory, artificial intelligence, and linguistics as recursive probabilistic programs and illustrate how this representation language makes it easy to explore new directions in each of these fields. We discuss the algorithmic challenges posed by these kinds of models and describe how dynamic programming techniques can help address these challenges. (C) 2014 Published by Elsevier B.V.

关键词： probabilistic programming Social cognition Recursive reasoning

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Prescribing product upgrades, prices and production levels over time in a stochastic environment

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第3期138卷 601-621页

作者： Wilhelm, WE Xu, KH Texas A&M Univ Dept Ind Engn College Stn TX 77843 USA

Competitive pressures cause the price of high-technology products to erode over time. The purpose of this paper is to describe a decision support tool to maximize profit by prescribing three related decisions: product upgrading. pricing and production levels. A stochastic dynamic programming (DP) model prescribes when to upgrade a product and what new technologies to incorporate to maintain product competitiveness and profit margins. It deals with the two major sources of risk: demand and the lead time required to complete an upgrade. The objective of the DP model is to maximize expected profit over a given planning horizon. Decision variables prescribe which alternative upgrades to implement and when, pricing, and production levels. Benchmarking computational tests are described along with an example demonstrating model application. Managers can use this DP model to coordinate decisions related to product upgrading, pricing, and operations management to better meet business objectives. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： manufacturing marketing product upgrading pricing probabilistic programming

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CUQIpy: II. Computational uncertainty quantification for PDE-based inverse problems in Python

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INVERSE PROBLEMS 2024年第4期40卷 045010-045010页

作者： Alghamdi, Amal M. A. Riis, Nicolai A. B. Afkham, Babak M. Uribe, Felipe Christensen, Silja L. Hansen, Per Christian Jorgensen, Jakob S. Tech Univ Denmark Richard Petersens Plads Dept Appl Math & Comp Sci Bldg 324 DK-2800 Kongens Lyngby Denmark Lappeenranta Lahti Univ Technol LUT Sch Engn Sci Yliopistonkatu 34 Lappeenranta 53850 Finland Univ Manchester Dept Math Oxford RdAlan Turing Bldg Manchester M13 9PL England

Inverse problems, particularly those governed by Partial Differential Equations (PDEs), are prevalent in various scientific and engineering applications, and uncertainty quantification (UQ) of solutions to these problems is essential for informed decision-making. This second part of a two-paper series builds upon the foundation set by the first part, which introduced CUQIpy, a Python software package for computational UQ in inverse problems using a Bayesian framework. In this paper, we extend CUQIpy's capabilities to solve PDE-based Bayesian inverse problems through a general framework that allows the integration of PDEs in CUQIpy, whether expressed natively or using third-party libraries such as FEniCS. CUQIpy offers concise syntax that closely matches mathematical expressions, streamlining the modeling process and enhancing the user experience. The versatility and applicability of CUQIpy to PDE-based Bayesian inverse problems are demonstrated on examples covering parabolic, elliptic and hyperbolic PDEs. This includes problems involving the heat and Poisson equations and application case studies in electrical impedance tomography and photo-acoustic tomography, showcasing the software's efficiency, consistency, and intuitive interface. This comprehensive approach to UQ in PDE-based inverse problems provides accessibility for non-experts and advanced features for experts.

关键词： uncertainty quantification software computational imaging Bayesian statistics probabilistic programming partial differential equations

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Mixed Nondeterministic-probabilistic Automata

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DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS 2023年第4期33卷 455-505页

作者： Benveniste, Albert Raclet, Jean-Baptiste Inria Rennes Bretagne Atlantique F-35042 Rennes France Univ Toulouse IRIT CNRS Toulouse INPUT3 Toulouse France

Graphical models in probability and statistics are a core concept in the area of probabilistic reasoning and probabilistic programming-graphical models include Bayesian networks and factor graphs. For modeling and formal verification of probabilistic systems, probabilistic automata were introduced. This paper proposes a coherent suite of models consisting of Mixed Systems, Mixed Bayesian Networks, and Mixed Automata, which extend factor graphs, Bayesian networks, and probabilistic automata with the handling of nondeterminism. Each of these models comes with a parallel composition, and we establish clear relations between these three models. Also, we provide a detailed comparison between Mixed Automata and probabilistic Automata

关键词： probabilistic automata Semantics Nondeterminism and probability Factor graphs Bayesian networks probabilistic programming

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Lifted graphical models: a survey

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MACHINE LEARNING 2015年第1期99卷 1-45页

作者： Kimmig, Angelika Mihalkova, Lilyana Getoor, Lise Katholieke Univ Leuven Dept Comp Sci Leuven Belgium Google Los Angeles CA USA Univ Calif Santa Cruz Dept Comp Sci Santa Cruz CA 95064 USA

Lifted graphical models provide a language for expressing dependencies between different types of entities, their attributes, and their diverse relations, as well as techniques for probabilistic reasoning in such multi-relational domains. In this survey, we review a general form for a lifted graphical model, a par-factor graph, and show how a number of existing statistical relational representations map to this formalism. We discuss inference algorithms, including lifted inference algorithms, that efficiently compute the answers to probabilistic queries over such models. We also review work in learning lifted graphical models from data. There is a growing need for statistical relational models (whether they go by that name or another), as we are inundated with data which is a mix of structured and unstructured, with entities and relations extracted in a noisy manner from text, and with the need to reason effectively with this data. We hope that this synthesis of ideas from many different research groups will provide an accessible starting point for new researchers in this expanding field.

关键词： Statistical relational learning First-order probabilistic models probabilistic programming Par-factor graphs Templated graphical models Lifted inference and learning

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A factor graph approach to automated design of Bayesian signal processing algorithms

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2019年 104卷 185-204页

作者： Cox, Marco van de Laar, Thijs de Vries, Bert Eindhoven Univ Technol Dept Elect Engn POB 513 NL-6500 MB Eindhoven Netherlands GN Hearing Eeuwsel 6 NL-5612 AS Eindhoven Netherlands

The benefits of automating design cycles for Bayesian inference-based algorithms are becoming increasingly recognized by the machine learning community. As a result, interest in probabilistic programming frameworks has much increased over the past few years. This paper explores a specific probabilistic programming paradigm, namely message passing in Forney-style factor graphs (FFGs), in the context of automated design of efficient Bayesian signal processing algorithms. To this end, we developed "ForneyLab("2) as a Julia toolbox for message passing-based inference in FFGs. We show by example how ForneyLab enables automatic derivation of Bayesian signal processing algorithms, including algorithms for parameter estimation and model comparison. Crucially, due to the modular makeup of the FFG framework, both the model specification and inference methods are readily extensible in FomeyLab. In order to test this framework, we compared variational message passing as implemented by ForneyLab with automatic differentiation variational inference (ADVI) and Monte Carlo methods as implemented by state-of-the-art tools "Edward" and "Stan". In terms of performance, extensibility and stability issues, ForneyLab appears to enjoy an edge relative to its competitors for automated inference in state-space models. (C) 2018 Elsevier Inc. All rights reserved.

关键词： probabilistic programming Bayesian inference Julia Factor graphs Message passing

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Automatic Differentiation in Prolog

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THEORY AND PRACTICE OF LOGIC programming 2023年第4期23卷 900-917页

作者： Schrijvers, Tom Van Den Berg, Birthe Riguzzi, Fabrizio Katholieke Univ Leuven Leuven Belgium Univ Ferrara Ferrara Italy

Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function's (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular as part of many learning algorithms, notably for neural networks. This paper uses Prolog to systematically derive gradient-based forward- and reverse-mode AD variants from a simple executable specification: evaluation of the symbolic derivative. Along the way we demonstrate that several Prolog features (DCGs, co-routines) contribute to the succinct formulation of the algorithm. We also discuss two applications in probabilistic programming that are enabled by our Prolog algorithms. The first is parameter learning for the Sum-Product Loop Language and the second consists of both parameter learning and variational inference for probabilistic logic programming.

关键词： Prolog automatic differentiation probabilistic programming

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DEVELOPMENT OF A STOCHASTIC-MODEL FOR THE ECONOMIC-DISPATCH OF ELECTRIC-POWER

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1986年第2期27卷 179-191页

作者： BUNN, DW PASCHENTIS, SN ORCO LTD ATHENS ATHENSGREECE

A large-scale model to support the online scheduling of power generation at 5 minute intervals is developed using a form of stochastic linear programming. This model takes explicit account of the expected recourse action which will be associated with the mismatch between dispatched generation and actual load demanded. Various experimental results on data for the S.W. Region of the CEGB demonstrate the economic efficiency of this approach over the more conventional deterministic linear programming model. [ABSTRACT FROM AUTHOR]

关键词： Energy probabilistic programming public service

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