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Affine Monads and Lazy Structures for Bayesian programming

PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2023年第POPL期7卷 1338-1368页

作者： Dash, Swaraj Kaddar, Younesse Paquet, Hugo Staton, Sam Univ Oxford Oxford England

We show that streams and lazy data structures are a natural idiom for programming with infinite-dimensional Bayesian methods such as Poisson processes, Gaussian processes, jump processes, Dirichlet processes, and Beta processes. The crucial semantic idea, inspired by developments in synthetic probability theory, is to work with two separate monads: an affine monad of probability, which supports laziness, and a commutative, non-affine monad of measures, which does not. (Affine means that T (1) congruent to 1.) We show that the separation is important from a decidability perspective, and that the recent model of quasi-Borel spaces supports these two monads. To perform Bayesian inference with these examples, we introduce new inference methods that are specially adapted to laziness;they are proven correct by reference to the Metropolis-Hastings-Green method. Our theoretical development is implemented as a Haskell library, LazyPPL.

关键词： Bayesian inference Haskell categorical semantics commutative monads functional programming laziness nonparametric statistics probabilistic programming quasi-Borel spaces synthetic measure theory

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Novel Bayesian Networks for Genomic Prediction of Developmental Traits in Biomass Sorghum

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G3-GENES GENOMES GENETICS 2020年第2期10卷 769-781页

作者： dos Santos, Jhonathan P. R. Fernandes, Samuel B. McCoy, Scott Lozano, Roberto Brown, Patrick J. Leakey, Andrew D. B. Buckler, Edward S. Garcia, Antonio A. F. Gore, Michael A. Cornell Univ Sch Integrat Plant Sci Plant Breeding & Genet Sect 358 Plant Sci Bldg Ithaca NY 14853 USA Cornell Univ Inst Genom Divers Ithaca NY 14853 USA Univ Sao Paulo Luiz de Queiroz Coll Agr Dept Genet Piracicaba SP Brazil Univ Illinois Dept Crop Sci Urbana IL 61801 USA Univ Illinois Inst Genom Biol Urbana IL 61801 USA Univ Illinois Dept Plant Biol Urbana IL 61801 USA Univ Calif Davis Dept Plant Sci Sect Agr Plant Biol Davis CA 95616 USA ARS USDA RW Holley Ctr Ithaca NY 14853 USA

The ability to connect genetic information between traits over time allow Bayesian networks to offer a powerful probabilistic framework to construct genomic prediction models. In this study, we phenotyped a diversity panel of 869 biomass sorghum (Sorghum bicolor (L.) Moench) lines, which had been genotyped with 100,435 SNP markers, for plant height (PH) with biweekly measurements from 30 to 120 days after planting (DAP) and for end-of-season dry biomass yield (DBY) in four environments. We evaluated five genomic prediction models: Bayesian network (BN), Pleiotropic Bayesian network (PBN), Dynamic Bayesian network (DBN), multi-trait GBLUP (MTr-GBLUP), and multi-time GBLUP (MTi-GBLUP) models. In fivefold cross-validation, prediction accuracies ranged from 0.46 (PBN) to 0.49 (MTr-GBLUP) for DBY and from 0.47 (DBN, DAP120) to 0.75 (MTi-GBLUP, DAP60) for PH. Forward-chaining cross-validation further improved prediction accuracies of the DBN, MTi-GBLUP and MTr-GBLUP models for PH (training slice: 30-45 DAP) by 36.4-52.4% relative to the BN and PBN models. Coincidence indices (target: biomass, secondary: PH) and a coincidence index based on lines (PH time series) showed that the ranking of lines by PH changed minimally after 45 DAP. These results suggest a two-level indirect selection method for PH at harvest (first-level target trait) and DBY (second-level target trait) could be conducted earlier in the season based on ranking of lines by PH at 45 DAP (secondary trait). With the advance of high-throughput phenotyping technologies, our proposed two-level indirect selection framework could be valuable for enhancing genetic gain per unit of time when selecting on developmental traits.

关键词： Bayesian networks biomass sorghum genomic prediction indirect selection probabilistic programming Genomic Prediction GenPred Shared Data Resources

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STOCHASTIC-programming IN WATER MANAGEMENT - A CASE-STUDY AND A COMPARISON OF SOLUTION TECHNIQUES

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1991年第1期52卷 28-44页

作者： DUPACOVA, J GAIVORONSKI, A KOS, Z SZANTAI, T VM GLUSHKOV CYBERNET INST KIEV 252207 UKRAINE USSR TECH UNIV PRAGUE FAC ENGN CS-16629 PRAGUE CZECHOSLOVAKIA EOTVOS LORAND UNIV DEPT OPERAT RES H-1088 BUDAPEST HUNGARY INT INST APPL SYST ANAL A-2361 LAXENBURG AUSTRIA

The present stage of developments in stochastic programming gives already a good base for real-life applications. The possibility of using alternative models is studied on a small-size but meaningful example connected with water management of a real-life water resource system in Eastern Czechoslovakia. Both of the considered conceptually different stochastic programming models take into account intercorrelations within a group of random parameters and provide comparable optimal decisions. At the same time, these models are used for comparison of existing numerical procedures for stochastic programming, namely, approximation schemes that result in large-size linear programs, stochastic quasigradient methods and special techniques for handling joint chance constraints.

关键词： WATER MANAGEMENT probabilistic programming STOCHASTIC QUASI-GRADIENT METHODS COMPUTATIONAL ANALYSIS STOCHASTIC MODELING

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THE CHANCE CONSTRAINED CRITICAL PATH WITH LOCATION SCALE DISTRIBUTIONS

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1984年第3期18卷 359-363页

作者： KRESS, M CEMA HAIFAISRAEL

The Chance Constrained Critical Path (CCCP) generally depends on the preassigned minimum probability level. It is shown that for a wide class of probability distributions there always exists a probability value for which the CCCP remains unchanged for all probabilities greater than or equal to that value. This probability value is easily obtained from an optimal solution of a simple network problem. In addition, necessary and sufficient conditions for the CCCP to be unconditionally independent of the minimum probability level are given for that class of probability distributions.

关键词： Critical path programming probabilistic programming

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MIP reformulations of the probabilistic set covering problem

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MATHEMATICAL programming 2010年第1期121卷 1-31页

作者： Saxena, Anureet Goyal, Vineet Lejeune, Miguel A. Drexel Univ LeBow Coll Business Philadelphia PA 19104 USA Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA

In this paper, we address the following probabilistic version (PSC) of the set covering problem: min{cx vertical bar P(Ax >= xi) >= p, x is an element of {0, 1}(N)} where A is a 0-1 matrix, xi is a random 0-1 vector and p is an element of (0, 1] is the threshold probability level. We introduce the concepts of p-inefficiency and polarity cuts. While the former is aimed at deriving an equivalent MIP reformulation of (PSC), the latter is used as a strengthening device to obtain a stronger formulation. Simplifications of the MIP model which result when one of the following conditions hold are briefly discussed: A is a balanced matrix, A has the circular ones property, the components of xi are pairwise independent, the distribution function of xi is a stationary distribution or has the disjunctive shattering property. We corroborate our theoretical findings by an extensive computational experiment on a test-bed consisting of almost 10,000 probabilistic instances. This test-bed was created using deterministic instances from the literature and consists of probabilistic variants of the set covering model and capacitated versions of facility location, warehouse location and k-median models. Our computational results show that our procedure is orders of magnitude faster than any of the existing approaches to solve (PSC), and in many cases can reduce hours of computing time to a fraction of a second.

关键词： probabilistic programming Set covering Mixed integer programming Cutting planes

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On the Probability and Cost of Ignorance, Inconsistency, Nonsense and More

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JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING 2020年第5-6期34卷 423-450页

作者： Szalas, Andrzej Univ Warsaw Dept Math Informat & Mech Warsaw Poland Univ Linkoping Dept Comp & Informat Sci Linkoping Sweden

Ignorance, inconsistency, nonsense and similar phenomena are omnipresent in everyday reasoning. They have been intensively studied, especially in the area of multiple-valued logics. Therefore we develop a framework for belief bases, combining multiple-valued and probabilistic reasoning, with the main focus on the way belief bases are actually used and accessed through queries. As an implementation tool we use a probabilistic programming language PROBLOG. Though based on distribution semantics with the independence assumption, we show how its constructs can successfully be used in implementing the considered logics and belief bases. In particular, we develop a technique for shifting probabilistic dependencies to the level of symbolic parts of belief bases. We also discuss applications of the framework in reasoning with Likert-type scales, widely exploited in questionnaire-based experimental research in psychology, economics, sociology, politics, public opinion measurements, and related areas.

关键词： Multiple-valued logics doxastic reasoning probabilistic reasoning probabilistic programming belief bases reasoning with uncertainty

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Ab-initio prediction and reliability of protein structural genomics by PROPAINOR algorithm

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COMPUTATIONAL BIOLOGY AND CHEMISTRY 2003年第3期27卷 241-252页

作者： Joshi, RR Jyothi, S Indian Inst Technol BJM Sch Biosci & Bioengn Bombay 400076 Maharashtra India Indian Inst Technol Dept Math Bombay 400076 Maharashtra India

We have formulated the ab-initio prediction of the 3D-structure of proteins as a probabilistic programming problem where the inter-residue 3D-distances are treated as random variables. Lower and upper bounds for these random variables and the corresponding probabilities are estimated by nonparametric statistical methods and knowledge-based heuristics. In this paper we focus on the probabilistic computation of the 3D-structure using these distance interval estimates. Validation of the predicted structures shows our method to be more accurate than other computational methods reported so far. Our method is also found to be computationally more efficient than other existing ab-initio structure prediction methods. Moreover, we provide a reliability index for the predicted structures too. Because of its computational simplicity and its applicability to any random sequence, our algorithm called PROPAINOR (PROtein structure Prediction by AI an Nonparametric Regression) has significant scope in computational protein structural genomics. (C) 2002 Published by Elsevier Science Ltd.

关键词： ab-initio protein structure prediction distance geometry nonparametric discriminant analysis nonpararnetric regression probabilistic programming reliability index

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A probability perspective

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FORMAL ASPECTS OF COMPUTING 2011年第4期23卷 391-419页

作者： Hehner, Eric C. R. Univ Toronto Dept Comp Sci Toronto ON M5S 2E4 Canada

This paper draws together four perspectives that contribute to a new understanding of probability and solving problems involving probability. The first is the Subjective Bayesian perspective that probability is affected by one's knowledge, and that it is updated as one's knowledge changes. The main criticism of the Bayesian perspective is the problem of assigning prior probabilities;this problem disappears with our Information Theory perspective, in which we take the bold new step of equating probability with information. The main point of the paper is that the formal perspective (formalize, calculate, unformalize) is beneficial to solving probability problems. And finally, the programmer's perspective provides us with a suitable formalism. To illustrate the benefits of these perspectives, we completely solve the hitherto open problem of the two envelopes.

关键词： Bayesian probability probabilistic programming Two envelopes

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Smoothness Analysis for probabilistic Programs with Application to Optimised Variational Inference

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2023年第POPL期7卷 335-366页

作者： Lee, Wonyeol Rival, Xavier Yang, Hongseok Stanford Univ Comp Sci Stanford CA 94305 USA INRIA Paris Paris France CNRS ENS Paris France PSL Univ Paris France Korea Adv Inst Sci & Technol Sch Comp Daejeon South Korea Korea Adv Inst Sci & Technol Kim Jaechul Grad Sch AI Daejeon South Korea Inst Basic Sci IBS Discrete Math Grp Daejeon South Korea

We present a static analysis for discovering differentiable or more generally smooth parts of a given probabilistic program, and show how the analysis can be used to improve the pathwise gradient estimator, one of the most popular methods for posterior inference and model learning. Our improvement increases the scope of the estimator from differentiable models to non-differentiable ones without requiring manual intervention of the user;the improved estimator automatically identifies differentiable parts of a given probabilistic program using our static analysis, and applies the pathwise gradient estimator to the identified parts while using a more general but less efficient estimator, called score estimator, for the rest of the program. Our analysis has a surprisingly subtle soundness argument, partly due to the misbehaviours of some target smoothness properties when viewed from the perspective of program analysis designers. For instance, some smoothness properties, such as partial differentiability and partial continuity, are not preserved by function composition, and this makes it difficult to analyse sequential composition soundly without heavily sacrificing precision. We formulate five assumptions on a target smoothness property, prove the soundness of our analysis under those assumptions, and showthat our leading examples satisfy these assumptions. We also showthat by using information from our analysis instantiated for differentiability, our improved gradient estimator satisfies an important differentiability requirement and thus computes the correct estimate on average (i.e., returns an unbiased estimate) under a regularity condition. Our experiments with representative probabilistic programs in the Pyro language show that our static analysis is capable of identifying smooth parts of those programs accurately, and making our improved pathwise gradient estimator exploit all the opportunities for high performance in those programs.

关键词： smoothness static analysis probabilistic programming variational inference

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Computing functions of random variables via reproducing kernel Hilbert space representations

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STATISTICS AND COMPUTING 2015年第4期25卷 755-766页

作者： Schoelkopf, Bernhard Muandet, Krikamol Fukumizu, Kenji Harmeling, Stefan Peters, Jonas Max Planck Inst Intelligent Syst D-72076 Tubingen Germany Inst Stat Math Tachikawa Tokyo Japan Univ Dusseldorf Inst Informat D-40225 Dusseldorf Germany Swiss Fed Inst Technol Seminar Stat CH-8092 Zurich Switzerland

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations which can be applied to points drawn from the respective distributions. We refer to our approach as kernel probabilistic programming. We illustrate it on synthetic data and show how it can be used for nonparametric structural equation models, with an application to causal inference.

关键词： Kernel methods probabilistic programming Causal inference

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