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ACM TRANSACTIONS ON EMBEDDED COMPUTING SYSTEMS 2021年第4期20卷 1–26页

作者： Broman, David KTH Royal Inst Technol Kistagangen 16 S-16440 Kista Sweden Digital Futures Osquars Backe 5Floor 2 S-10044 Stockholm Sweden

Modeling and computational analyses are fundamental activities within science and engineering. Analysis activities can take various forms, such as simulation of executable models, formal verification of model properties, or inference of hidden model variables. Traditionally, tools for modeling and analysis have similar workflows: (i) a user designs a textual or graphical model or the model is inferred from data, (ii) a tool performs computational analyses on the model, and (iii) a visualization tool displays the resulting data. This article identifies three inherent problems with the traditional approach: the recomputation problem, the variable inspection problem, and the model expressiveness problem. As a solution, we propose a conceptual framework called Interactive Programmatic Modeling. We formalize the interface of the framework and illustrate how it can be used in two different domains: equation-based modeling and probabilistic programming.

关键词： Modeling languages cyber-physical systems probabilistic programming

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Modeling the shelter site location problem using chance constraints: A case study for Istanbul

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第1期270卷 132-145页

作者： Kinay, Omer Burak Kara, Bahar Yetis Saldanha-da-Gama, Francisco Correia, Isabel Univ Waterloo Dept Management Sci Waterloo ON Canada Bilkent Univ Dept Ind Engn Ankara Turkey Univ Lisbon Dept Estat & Invest Operac Ctr Matemat Aplicaes Fundamentais & Invest Operac Fac Ciencias P-1749016 Lisbon Portugal Univ Nova Lisboa Fac Ciencias & Tecnol Dept Matemat Ctr Matemat & Aplicacoes P-2829516 Caparica Portugal

In this work, we develop and test a new modeling framework for the shelter site location problem under demand uncertainty. In particular, we propose a maxmin probabilistic programming model that includes two types of probabilistic constraints: one concerning the utilization rate of the selected shelters and the other concerning the capacity of those shelters. By invoking the central limit theorem we are able to obtain an optimization model with a single set of non-linear constraints which, nonetheless, can be approximated using a family of piecewise linear functions. The latter, in turn, can be modeled mathematically using integer variables. Eventually, an approximate model is obtained, which is a mixed-integer linear programming model that can be tackled by an off-the-shelf solver. Using the proposed reformulation we are able to solve instances of the problem using data associated with the Kartal district in Istanbul, Turkey. We also consider a large-scale instance of the problem by making use of data for the whole Anatolian side of Istanbul. The results obtained are presented and discussed in the paper. They provide clear evidence that capturing uncertainty in the shelter site location problem by means of probabilistic constraints may lead to solutions that are much different from those obtained when a deterministic counterpart is considered. Furthermore, it is possible to observe that the probabilities embedded in the probabilistic constraints have a clear influence in the results, thus supporting the statement that a probabilistic programming modeling framework, if appropriately tuned by a decision maker, can make a full difference when it comes to find good solutions for the problem. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Location Humanitarian logistics Shelter site location probabilistic programming Approximations

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Automatic Differentiation Variational Inference

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JOURNAL OF MACHINE LEARNING RESEARCH 2017年第1期18卷 1-45页

作者： Kucukelbir, Alp Tran, Dustin Ranganath, Rajesh Gelman, Andrew Blei, David M. Columbia Univ Dept Comp Sci Data Sci Inst New York NY 10027 USA Columbia Univ Dept Comp Sci New York NY 10027 USA Princeton Univ Dept Comp Sci Princeton NJ 08540 USA Columbia Univ Data Sci Inst Dept Polit Sci New York NY 10027 USA Columbia Univ Data Sci Inst Dept Stat New York NY 10027 USA

probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving algorithms for new models can be both mathematically and computationally challenging, which makes it difficult to efficiently cycle through the steps. To this end, we develop automatic differentiation variational inference (ADVI). Using our method, the scientist only provides a probabilistic model and a dataset, nothing else. ADVI automatically derives an efficient variational inference algorithm, freeing the scientist to refine and explore many models. ADVI supports a broad class of models-no conjugacy assumptions are required. We study ADVI across ten modern probabilistic models and apply it to a dataset with millions of observations. We deploy ADVI as part of Stan, a probabilistic programming system.

关键词： Bayesian inference approximate inference probabilistic programming

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Debugging convergence problems in probabilistic programs via program representation learning with SixthSense

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INTERNATIONAL JOURNAL ON SOFTWARE TOOLS FOR TECHNOLOGY TRANSFER 2024年第3期26卷 249-268页

作者： Huang, Zixin Dutta, Saikat Misailovic, Sasa Univ Illinois Dept Comp Sci 201 North Goodwin Ave Urbana IL 61801 USA Cornell Univ Dept Comp Sci 402 Gates Hall Ithaca NY 14853 USA

probabilistic programming aims to open the power of Bayesian reasoning to software developers and scientists, but identification of problems during inference and debugging are left entirely to the developers and typically require significant statistical expertise. A common class of problems when writing probabilistic programs is the lack of convergence of the probabilistic programs to their posterior *** present SixthSense, a novel approach for predicting probabilistic program convergence ahead of run and its application to debugging convergence problems in probabilistic programs. SixthSense's training algorithm learns a classifier that can predict whether a previously unseen probabilistic program will converge. It encodes the syntax of a probabilistic program as motifs - fragments of the syntactic program paths. The decisions of the classifier are interpretable and can be used to suggest the program features that contributed significantly to program convergence or non-convergence. We also present an algorithm for augmenting a set of training probabilistic programs that uses guided *** evaluated SixthSense on a broad range of widely used probabilistic programs. Our results show that SixthSense features are effective in predicting convergence of programs for given inference algorithms. SixthSense obtained accuracy of over 78% for predicting convergence, substantially above the state-of-the-art techniques for predicting program properties Code2Vec and Code2Seq. We show the ability of SixthSense to guide the debugging of convergence problems, which pinpoints the causes of non-convergence significantly better by Stan's built-in warnings.

关键词： probabilistic programming Debugging Machine learning

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Solution to the practical problem of moments using non-classical orthogonal polynomials, with applications for probabilistic analysis

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probabilistic ENGINEERING MECHANICS 2000年第4期15卷 371-379页

作者： Kennedy, CA Lennox, WC Univ Toronto Dept Civil Engn Toronto ON M5S 1A4 Canada Univ Waterloo Dept Civil Engn Waterloo ON N2L 3G1 Canada

A method is presented for solving the "practical" problem of moments to produce probability density functions (PDFs) using non-classical orthogonal polynomials. PDFs are determined from given sets of moments by applying the Gram-Schmidt process with the aid of computer algebra. By selecting weighting functions of similar shape to desired PDFs, orthogonal polynomial series are obtained that are stable at high order and allow accurate approximation of tail probabilities. The method is first demonstrated by approximating a chi(2) PDF with an orthogonal series based on a lognormal weighting function. More general orthogonal expansions, based on Pearson type I and Johnson transform distributions, are then demonstrated. These expansions are used to produce PDFs for maximum daily river discharge, concrete strength, and maximum seasonal snow depths, using Limited data sets. In all three cases the moments of the high order series are found to closely match those of the data. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： probabilistic programming problem of moments extreme events orthogonal polynomials

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A Theory of Slicing for Imperative probabilistic Programs

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ACM TRANSACTIONS ON programming LANGUAGES AND SYSTEMS 2020年第2期42卷 6-6页

作者： Amtoft, Torben Banerjee, Anindya Kansas State Univ Dept Comp Sci 2184 Engn Hall1701D Platt St Manhattan KS 66506 USA IMDEA Software Inst Campus Montegancedo S-N Madrid 28223 Spain

Dedicated to the memory of Sebastian Danicic. We present a theory for slicing imperative probabilistic programs containing random assignments and "observe" statements for conditioning. We represent such programs as probabilistic control-flow graphs (pCFGs) whose nodes modify probability distributions. This allows direct adaptation of standard machinery such as data dependence, postdominators, relevant variables, and so on, to the probabilistic setting. We separate the specification of slicing from its implementation: (1) first, we develop syntactic conditions that a slice must satisfy (they involve the existence of another disjoint slice such that the variables of the two slices are probabilistically independent of each other);(2) next, we prove that any such slice is semantically correct;(3) finally, we give an algorithm to compute the least slice. To generate smaller slices, we may in addition take advantage of knowledge that certain loops will terminate (almost) always. Our results carry over to the slicing of structured imperative probabilistic programs, as handled in recent work by Hur et al. For such a program, we can define its slice, which has the same "normalized" semantics as the original program;the proof of this property is based on a result proving the adequacy of the semantics of pCFGs w.r.t. the standard semantics of structured imperative probabilistic programs.

关键词： probabilistic programming program slicing probabilistic control-flow graphs

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InferPy: probabilistic modeling with Tensorflow made easy

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KNOWLEDGE-BASED SYSTEMS 2019年 168卷 25-27页

作者： Cabanas, Rafael Salmeron, Antonio Masegosa, Andres R. Univ Almeria ES-04120 Almeria Spain

InferPy is a high-level Python API for probabilistic modeling built on top of Edward and Tensorflow. InferPy, which is strongly inspired by Keras, focuses on being user-friendly by using an intuitive set of abstractions that make easy to deal with complex probabilistic models. It should be seen as an interface rather than a standalone machine-learning framework. In general, InferPy has the focus on enabling flexible data processing, easy-to-code probabilistic modeling, scalable inference and robust model validation. (C) 2019 Elsevier B.V. All rights reserved.

关键词： probabilistic programming Hierarchical probabilistic models Latent variables Tensorflow User-friendly

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On joint probabilistic constraints with Gaussian coefficient matrix

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OPERATIONS RESEARCH LETTERS 2011年第2期39卷 99-102页

作者： van Ackooij, W. Henrion, R. Moeller, A. Zorgati, R. Weierstrass Inst D-10117 Berlin Germany Elect France R&D F-92141 Clamart France

The paper deals with joint probabilistic constraints defined by a Gaussian coefficient matrix. It is shown how to explicitly reduce the computation of values and gradients of the underlying probability function to that of Gaussian distribution functions. This allows us to employ existing efficient algorithms for calculating this latter class of functions in order to solve probabilistically constrained optimization problems of the indicated type. Results are illustrated by an example from energy production. (c) 2011 Elsevier B.V. All rights reserved.

关键词： probabilistic constraint Chance constraint Gaussian coefficient matrix gradient formula probabilistic programming Stochastic optimization Energy portfolio optimization

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The effect of building attributes on the energy performance at a scale: an inferential analysis

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BUILDING RESEARCH AND INFORMATION 2022年第6期50卷 662-680页

作者： Zhuravchak, Ruslan Nord, Natasa Brattebo, Helge NTNU Dept Energy & Proc Engn Kolbjorn Hejes V 1B Trondheim Norway

The commitments to mitigate the negative impacts associated with final energy use stipulate the increase of energy efficiency of the built environment. This is the focus of urban energy policies and of built stock energy models that aid them. The complexities behind the phenomenon, however, hinder the development of the means for controlling and unbiased modelling. Such tasks necessitate the empirical evidence of causal relationships between architectural and technical attributes and building energy performance at the population level. This study, therefore, elaborates on the methods of inferential statistics for establishing such causal effects. The focus is on the methods of frequentist inference, active use of which may advance the understanding of the phenomenon and foster more accurate modelling practices. The case study examines the energy performance exhibited by distinct configurations of construction periods, envelope materials, sources of energy for space heating and the ventilation system types. The empirical sample consists of more than 11,000 records registered in the Norwegian energy performance certification system. The results document the effects and their significance. These methods are applicable in any urban context and may provide the empirical basis for promoting/discouraging certain technological and architectural tendencies, and simulating the phenomena through probabilistic programming.

关键词： Built stock energy performance probabilistic programming combinatorial analysis frequentist inference univariate density estimation statistical hypothesis testing

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Long-term electricity contract optimization with demand uncertainties

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ENERGY 2006年第13期31卷 2469-2485页

作者： Chan, Pang Hui, Chi-Wai Li, Wenkai Sakamoto, Haruo Hirata, Kentaro Li, Pu Hong Kong Univ Sci & Technol Dept Chem Engn Hong Kong Hong Kong Peoples R China Mitsubishi Chem Grp Proc Syst Engn & Prod Technol Res & Technol Dev Div Proc Dev & Design LabProc Syst Engn & Prod Techn Yokaichi Mie 5108530 Japan Tech Univ Berlin Inst Prozess & Anlagentech KWT9 D-10623 Berlin Germany

This paper presents a study on selecting electricity contracts for a large-scale chemical production plant, which requires electricity importation, under demand uncertainty. Two common types of electricity contracts are considered, time zone (TZ) contract and loading curve (LC) contract. A multi-period linear probabilistic programming model is adopted for the contract selection and optimization. Hence, by using the probabilistic programming, a solution procedure is proposed that allow users to determine the best electricity contract according to their desired confident level of the uncertainties. In addition, due to the fact that the demand of product is uncertain, if one considers the overage and shortage of the products in the market as well, an interesting result can be obtained. The methodology is explained in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： electricity contract optimization uncertainty probabilistic programming confidence level

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