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ECOLOGY AND EVOLUTION 2021年第20期11卷 14101-14114页

作者： Laitinen, Ville Dakos, Vasilis Lahti, Leo Univ Turku Dept Comp Turku Finland Univ Montpellier Inst Sci Evolut Montpellier ISEM Montpellier France

Ecological communities and other complex systems can undergo abrupt and long-lasting reorganization, a regime shift, when deterministic or stochastic factors bring them to the vicinity of a tipping point between alternative states. Such changes can be large and often arise unexpectedly. However, theoretical and experimental analyses have shown that changes in correlation structure, variance, and other standard indicators of biomass, abundance, or other descriptive variables are often observed prior to a state shift, providing early warnings of an anticipated transition. Natural systems manifest unknown mixtures of ecological and environmental processes, hampered by noise and limited observations. As data quality often cannot be improved, it is important to choose the best modeling tools available for the analysis. We investigate three autoregressive models and analyze their theoretical differences and practical performance. We formulate a novel probabilistic method for early warning signal detection and demonstrate performance improvements compared to nonprobabilistic alternatives based on simulation and publicly available experimental time series. The probabilistic formulation provides a novel approach to early warning signal detection and analysis, with enhanced robustness and treatment of uncertainties. In real experimental time series, the new probabilistic method produces results that are consistent with previously reported findings. Robustness to uncertainties is instrumental in the common scenario where mechanistic understanding of the complex system dynamics is not available. The probabilistic approach provides a new family of robust methods for early warning signal detection that can be naturally extended to incorporate variable modeling assumptions and prior knowledge.

关键词： early warning signals probabilistic programming

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Statically Bounded-Memory Delayed Sampling for probabilistic Streams

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2021年第OOPSLA期5卷 1–28页

作者： Atkinson, Eric Baudart, Guillaume Mandel, Louis Yuan, Charles Carbin, Michael MIT Cambridge MA 02139 USA PSL Univ INRIA Ecole Normale Super Paris France MIT IBM Watson AI Lab IBM Res Cambridge MA USA

probabilistic programming languages aid developers performing Bayesian inference. These languages provide programming constructs and tools for probabilistic modeling and automated inference. Prior work introduced a probabilistic programming language, ProbZelus, to extend probabilistic programming functionality to unbounded streams of data. This work demonstrated that the delayed sampling inference algorithm could be extended to work in a streaming context. ProbZelus showed that while delayed sampling could be effectively deployed on some programs, depending on the probabilistic model under consideration, delayed sampling is not guaranteed to use a bounded amount of memory over the course of the execution of the program. In this paper, we the present conditions on a probabilistic program's execution under which delayed sampling will execute in bounded memory. The two conditions are dataflow properties of the core operations of delayed sampling: the m-consumed property and the unseparated paths property. A program executes in bounded memory under delayed sampling if, and only if, it satisfies the m-consumed and unseparated paths properties. We propose a static analysis that abstracts over these properties to soundly ensure that any program that passes the analysis satisfies these properties, and thus executes in bounded memory under delayed sampling.

关键词： probabilistic programming reactive programming streaming inference semantics program analysis

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Equivalence and Similarity Refutation for probabilistic Programs

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2024年第PLDI期8卷 2098-2122页

作者： Chatterjee, Krishnendu Goharshady, Ehsan Kafshdar Novotny, Petr Zikelic, Dorde Inst Sci & Technol Austria ISTA Klosterneuburg Austria Masaryk Univ Brno Czech Republic Singapore Management Univ Singapore Singapore

We consider the problems of statically refuting equivalence and similarity of output distributions defined by a pair of probabilistic programs. Equivalence and similarity are two fundamental relational properties of probabilistic programs that are essential for their correctness both in implementation and in compilation. In this work, we present a new method for static equivalence and similarity refutation. Our method refutes equivalence and similarity by computing a function over program outputs whose expected value with respect to the output distributions of two programs is different. The function is computed simultaneously with an upper expectation supermartingale and a lower expectation submartingale for the two programs, which we show to together provide a formal certificate for refuting equivalence and similarity. To the best of our knowledge, our method is the first approach to relational program analysis to offer the combination of the following desirable features: (1) it is fully automated, (2) it is applicable to infinite-state probabilistic programs, and (3) it provides formal guarantees on the correctness of its results. We implement a prototype of our method and our experiments demonstrate the effectiveness of our method to refute equivalence and similarity for a number of examples collected from the literature.

关键词： probabilistic programming Static program analysis Probability distribution equivalence Kantorovich distance Martingales

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Formal Verification of Higher-Order probabilistic Programs

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2019年第POPL期3卷 1-30页

作者： Sato, Tetsuya Aguirre, Alejandro Barthe, Gilles Gaboardi, Marco Garg, Deepak Hsu, Justin Univ Buffalo SUNY Buffalo NY 14260 USA IMDEA Software Inst Madrid Spain Max Planck Inst Software Syst Saarbrucken Germany Univ Wisconsin Madison WI USA

probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru, derive their expressiveness from a powerful combination of continuous distributions, conditioning, and higher-order functions. Although very important for practical applications, these features raise fundamental challenges for program semantics and verification. Several recent works offer promising answers to these challenges, but their primary focus is on foundational semantics issues. In this paper, we take a step further by developing a suite of logics, collectively named PPV, for proving properties of programs written in an expressive probabilistic higher-order language with continuous sampling operations and primitives for conditioning distributions. Our logics mimic the comfortable reasoning style of informal proofs using carefully selected axiomatizations of key results from probability theory. The versatility of our logics is illustrated through the formal verification of several intricate examples from statistics, probabilistic inference, and machine learning. We further show expressiveness by giving sound embeddings of existing logics. In particular, we do this in a parametric way by showing how the semantics idea of (unary and relational) TT-lifting can be internalized in our logics. The soundness of PPV follows by interpreting programs and assertions in quasi-Borel spaces (QBS), a recently proposed variant of Borel spaces with a good structure for interpreting higher order probabilistic programs.

关键词： probabilistic programming formal reasoning relational type systems

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Semantics of Higher-Order probabilistic Programs with Conditioning

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2020年第POPL期4卷 1–29页

作者： Dahlqvist, Fredrik Kozen, Dexter UCL Comp Sci London England Imperial Coll London Elect & Elect Engn London England Cornell Univ Comp Sci Ithaca NY USA

We present a denotational semantics for higher-order probabilistic programs in terms of linear operators between Banach spaces. Our semantics is rooted in the classical theory of Banach spaces and their tensor products, but bears similarities with the well-known semantics of higher-order programs a la Scott through the use of ordered Banach spaces which allow definitions in terms of fixed points. Our semantics is a model of intuitionistic linear logic: it is based on a symmetric monoidal closed category of ordered Banach spaces which treats randomness as a linear resource, but by constructing an exponential comonad we can also accommodate non-linear reasoning. We apply our semantics to the verification of the classical Gibbs sampling algorithm.

关键词： probabilistic programming semantics type system

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FairSquare: probabilistic Verification of Program Fairness

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2017年第OOPSLA期1卷 1-30页

作者： Albarghouthi, Aws D'Antoni, Loris Drews, Samuel Nori, Aditya, V Univ Wisconsin Dept Comp Sci 1210 West Dayton St Madison WI 53706 USA Microsoft Res 21 Stn Rd Cambridge CB1 2FB England

With the range and sensitivity of algorithmic decisions expanding at a break-neck speed, it is imperative that we aggressively investigate fairness and bias in decision-making programs. First, we show that a number of recently proposed formal definitions of fairness can be encoded as probabilistic program properties. Second, with the goal of enabling rigorous reasoning about fairness, we design a novel technique for verifying probabilistic properties that admits a wide class of decision-making programs. Third, we present FairSquare, the first verification tool for automatically certifying that a program meets a given fairness property. We evaluate FairSquare on a range of decision-making programs. Our evaluation demonstrates FairSquare's ability to verify fairness for a range of different programs, which we show are out-of-reach for state-of-the-art program analysis techniques.

关键词： Algorithmic Fairness probabilistic programming probabilistic Inference

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Machine-learning for biopharmaceutical batch process monitoring with limited data

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IFAC-PapersOnLine 2018年第18期51卷 126-131页

作者： Tulsyan, Aditya Garvin, Christopher Undey, Cenk Digital Integration & Predictive Technologies Amgen Inc. 360 Binney Street CambridgeMA02141 United States Digital Integration & Predictive Technologies Amgen Inc. 40 Technology Way West GreenwichRI02817 United States Digital Integration & Predictive Technologies Amgen Inc. One Amgen Center Drive Thousand OaksCA91320 United States

Commercial biopharmaceutical manufacturing comprises of multiple distinct processing steps that require effective and efficient monitoring of many variables simultaneously in real-time. This article addresses the problem of real-time statistical batch process monitoring (BPM) for biopharmaceutical processes with limited production history; herein, referred to as the ‘Low-N’ problem. In this article, we propose an approach to transition from a Low-N scenario to a Large-N scenario by generating an arbitrarily large number of in silico batch data sets. The proposed method is a combination of hardware exploitation and algorithm development. To this effect, we propose a Bayesian non-parametric approach to model a batch process, and then use probabilistic programming to generate an arbitrarily large number of dynamic in silico campaign data sets. The efficacy of the proposed solution is elucidated on an industrial process. © 2018

关键词： Batch data processing Learning systems Process control Process monitoring Algorithm development Batch process monitoring Efficient monitoring Industrial processs Low N problem Nonparametric approaches probabilistic programming Statistical batch process monitoring

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COAL BLENDING OPTIMIZATION UNDER UNCERTAINTY

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1995年第3期83卷 452-465页

作者： SHIH, JS FREY, HC N CAROLINA STATE UNIV DEPT CIVIL ENGNRALEIGHNC 27695

Coal blending is one of several options available for reducing sulfur emissions from coal-fired power plants. However, decisions about coal blending must deal with uncertainty and variability in coal properties, and with the effect of off-design coal characteristics on power plant performance and cost. To deal with these issues, a multi-objective chance-constrained optimization model is developed for an illustrative coal blending problem. Sulfur content, ash content and heating value are treated as normally distributed random variables. The objectives of the model include minimizing the: 1) expected (mean) costs of coal blending;2) standard deviation of coal blending costs;3) expected sulfur emissions;and 4) standard deviation in sulfur emissions. The cost objective function includes coal purchasing cost, ash disposal cost, sulfur removal cost, and fuel switching costs. Chance constraints include several risk measures, such as the probability of exceeding the sulfur emission standard. Several results are presented to illustrate the model.

关键词： ENERGY ENVIRONMENT probabilistic programming MULTIOBJECTIVE programming

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Compiling probabilistic Programs for Variable Elimination with Information Flow

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2024年第PLDI期8卷 1755-1780页

作者： Li, Jianlin Wang, Eric Zhang, Yizhou Univ Waterloo Waterloo ON Canada

A key promise of probabilistic programming is the ability to specify rich models using an expressive programming language. However, the expressive power that makes probabilistic programming languages enticing also poses challenges to inference, so much so that specialized approaches to inference ban language features such as recursion. We present an approach to variable elimination and marginal inference for probabilistic programs featuring bounded recursion, discrete distributions, and sometimes continuous distributions. A compiler eliminates probabilistic side effects, using a novel information-flow type system to factorize probabilistic computations and hoist independent subcomputations out of sums or integrals. For a broad class of recursive programs with dynamically recurring substructure, the compiler effectively decomposes a global marginal-inference problem, which may otherwise be intractable, into tractable subproblems. We prove the compilation correct by showing that it preserves denotational semantics. Experiments show that the compiled programs subsume widely used PTIME algorithms for recursive models and that the compilation time scales with the size of the inference problems. As a separate contribution, we develop a denotational, logical-relations model of information-flow types in the novel measure-theoretic setting of probabilistic programming;we use it to prove noninterference and consequently the correctness of variable elimination.

关键词： probabilistic programming probabilistic inference information flow

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Affine Monads and Lazy Structures for Bayesian programming

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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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