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Conditioning in probabilistic programming

ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 2015年 319卷 199-216页

作者： Benjamin, Nils Jansen Kaminski, Lucien Katoen, Joost-Pieter Olmedo, Federico Gretz, Friedrich McIver, Annabelle Rhein Westfal TH Aachen Aachen Germany Macquarie Univ Sydney NSW 2109 Australia

In this paper, we investigate the semantic intricacies of conditioning in probabilistic programming, a major feature, e.g., in machine learning. We provide a quantitative weakest pre-condition semantics. In contrast to all other approaches, non-termination is taken into account by our semantics. We also present an operational semantics in terms of Markov models and show that expected rewards coincide with quantitative pre-conditions. A program transformation that entirely eliminates conditioning from programs is given;the correctness is shown using our semantics. Finally, we show that an inductive semantics for conditioning in non-deterministic probabilistic programs cannot exist.

关键词： probabilistic programming Semantics Conditional Probabilities Program Transformation

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Multi-choice goal programming approach to solve multi-objective probabilistic programming problem

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JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2018年第3期39卷 607-629页

作者： Patro, Kanan K. Acharya, M. M. Acharya, S. KIIT Univ Sch Appl Sci Dept Math Bhubaneswar 751024 Odisha India Kendriya Vidyalaya Rayagada Dept Math Rayagada 765002 Odisha India

Stochastic programming is an art of modeling optimization problems in an environment, where randomness occurs. In this manuscript, we present a multi-objective probabilistic programming problem, where the random parameter follow logistic distribution. We transform the probabilistic programming model to an equivalent deterministic mathematical model by using chance constrained technique. Multiple number of aspiration levels are allocated to the objective function by Decision maker, the main aim is to obtain such a decision. After allocating several aspiration levels to the objective function, which will provide minimum deviation from objective function and aspiration level. Such minimization of deviation is possible by using multi-choice goal programming technique. Multi-choice parameters are handled by three different techniques viz;binary variable approach, Vandermonde's interpolating polynomial approach and linear least square approximation approach. To illustrate the methodology, a numerical example is presented.

关键词： probabilistic programming multi-choice goal programming multiple aspiration levels logistic distribution

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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 3-3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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StarfishDB: A Query Execution Engine for Relational probabilistic programming

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Proceedings of the ACM on Management of Data 2024年第3期2卷 1-31页

作者： Ouael Ben Amara Sami Hadouaj Niccolò Meneghetti Computer and Information Science (CIS) University of Michigan-Dearborn Dearborn MI USA

We introduce StarfishDB, a query execution engine optimized for relational probabilistic programming. Our engine adopts the model of Gamma probabilistic Databases, representing probabilistic programs as a collection of relational constraints, imposed against a generative stochastic process. We extend the model with the support for recursion, factorization and the ability to leverage just-in-time compilation techniques to speed up inference. We test our engine against a state-of-the-art sampler for Latent Dirichlet Allocation.

关键词： Bayesian inference probabilistic databases probabilistic programming

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Exploring Bayesian Approaches to eQTL Mapping Through probabilistic programming

Exploring Bayesian Approaches to eQTL Mapping Through Probab...

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作者： Dimitrios V. Vavoulis

The discovery of genomic polymorphisms influencing gene expression (also known as expression quantitative trait loci or eQTLs) can be formulated as a sparse Bayesian multivariate/multiple regression problem. An important aspect in the development of such models is the implementation of bespoke inference methodologies, a process which can become quite laborious, when multiple candidate models are being considered. We describe automatic, black-box inference in such models using Stan, a popular probabilistic programming language. The utilization of systems like Stan can facilitate model prototyping and testing, thus accelerating the data modeling process. The code described in this chapter can be found at https://***/dvav/eQTLBookChapter. less

关键词： RNA-seq Statistical Calculation programming Language R Stan eQTL mapping Bayesian variable selection Global-local shrinkage Horseshoe prior probabilistic programming Black-box Bayesian inference

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probabilistic logic programming for hybrid relational domains

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MACHINE LEARNING 2016年第3期103卷 407-449页

作者： Nitti, Davide De Laet, Tinne De Raedt, Luc Katholieke Univ Leuven Dept Comp Sci Leuven Belgium Katholieke Univ Leuven Fac Engn Sci Leuven Belgium

We introduce a probabilistic language and an efficient inference algorithm based on distributional clauses for static and dynamic inference in hybrid relational domains. Static inference is based on sampling, where the samples represent (partial) worlds (with discrete and continuous variables). Furthermore, we use backward reasoning to determine which facts should be included in the partial worlds. For filtering in dynamic models we combine the static inference algorithm with particle filters and guarantee that the previous partial samples can be safely forgotten, a condition that does not hold in most logical filtering frameworks. Experiments show that the proposed framework can outperform classic sampling methods for static and dynamic inference and that it is promising for robotics and vision applications. In addition, it provides the correct results in domains in which most probabilistic programming languages fail.

关键词： probabilistic programming Statistical relational learning Discrete and continuous distributions Particle filter Likelihood weighting Logic programming

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A probabilistic programming Approach for Outlier Detection in Healthcare Claims

A Probabilistic Programming Approach for Outlier Detection i...

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IEEE International Conference on Machine Learning and Applications

作者： Richard A. Bauder Taghi M. Khoshgoftaar Florida Atlantic University

ISBN: (纸本)9781509061686

Healthcare is an integral component in people's lives, especially for the rising elderly population. Medicare is one such healthcare program that provides for the needs of the elderly. It is imperative that these healthcare programs are affordable, but this is not always the case. Out of the many possible factors for the rising cost of healthcare, claims fraud is a major contributor, but its impact can be lessened through effective fraud detection. We propose a general outlier detection model, based on Bayesian inference, using probabilistic programming. Our model provides probability distributions rather than just point values, as with most common outlier detection methods. Credible intervals are also generated to further enhance confidence that the detected outliers should in fact be considered outliers. Two case studies are presented demonstrating our model's effectiveness in detecting outliers. The first case study uses temperature data in order to provide a clear comparison of several outlier detection techniques. The second case study uses a Medicare dataset to showcase our proposed outlier detection model. Our results show that the successful detection of outliers, which indicate possible fraudulent activities, can provide effective and meaningful results for further investigation within medical specialties or by using real-world, medical provider fraud investigation cases.

关键词： Fraud Detection Outlier Detection Healthcare Fraud Bayesian Inference probabilistic programming

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ProbLog2: probabilistic Logic programming

ProbLog2: Probabilistic Logic Programming

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European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD)

作者： Dries, Anton Kimmig, Angelika Meert, Wannes Renkens, Joris Van den Broeck, Guy Vlasselaer, Jonas De Raedt, Luc Katholieke Univ Leuven Leuven Belgium

ISBN: (纸本)9783319234618;9783319234601

We present ProbLog2, the state of the art implementation of the probabilistic programming language ProbLog. The ProbLog language allows the user to intuitively build programs that do not only encode complex interactions between a large sets of heterogenous components but also the inherent uncertainties that are present in real-life situations. The system provides efficient algorithms for querying such models as well as for learning their parameters from data. It is available as an online tool on the web and for download. The offline version offers both command line access to inference and learning and a Python library for building statistical relational learning applications from the system's components.

关键词： probabilistic programming probabilistic inference Parameter learning

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Multi-choice probabilistic linear programming problem

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OPSEARCH 2017年第1期54卷 122-142页

作者： Pradhan, Avik Biswal, M. P. Indian Inst Technol Kharagpur Dept Math Kharagpur 721302 W Bengal India

In this paper, we present a linear programming model where the parameter space contains some multi-choice parameters. Alternative choices of multi-choice parameter are considered as random variables. Using interpolating polynomial for each multi-choice parameter, the model has been transformed into a non-linear mixed integer probabilistic programming problem. Then chance constrained programming technique is used to obtain an equivalent deterministic model of the transformed problem. To find the deterministic form of the objective function four different models namely, E-model, V-model, probability maximization model and fractile criterion model are used. Assuming the values of the multi-choice parameters as independent normal random variables, the methodology is presented. A numerical example is also presented to illustrate the methodology.

关键词： Chance-constrained programming Multi-choice programming Linear programming probabilistic programming

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Declarative probabilistic logic programming in discrete-continuous domains

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ARTIFICIAL INTELLIGENCE 2024年 337卷

作者： Dos Martires, Pedro Zuidberg De Raedt, Luc Kimmig, Angelika Orebro Univ Ctr Appl Autonomous Sensor Syst Orebro Sweden Katholieke Univ Leuven Dept Comp Sci Leuven Belgium Leuven AI Leuven Belgium

Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming languages owes much of its success to a declarative semantics, the so-called distribution semantics. However, the distribution semantics is limited to discrete random variables only. While PLP has been extended in various ways for supporting hybrid, that is, mixed discrete and continuous random variables, we are still lacking a declarative semantics for hybrid PLP that not only generalizes the distribution semantics and the modeling language but also the standard inference algorithm that is based on knowledge compilation. We contribute the measure semantics together with the hybrid PLP language DC-ProbLog (where DC stands for distributional clauses) and its inference engine infinitesimal algebraic likelihood weighting (IALW). These have the original distribution semantics, standard PLP languages such as ProbLog, and standard inference engines for PLP based on knowledge compilation as special cases. Thus, we generalize the state of the art of PLP towards hybrid PLP in three different aspects: semantics, language and inference. Furthermore, IALW is the first inference algorithm for hybrid probabilistic programming based on knowledge compilation.

关键词： probabilistic programming Declarative semantics Discrete-continuous distributions Likelihood weighting Logic programming Knowledge compilation Algebraic model counting

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