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Higher-Order probabilistic Adversarial Computations: Categorical Semantics and Program Logics

PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2021年第ICFP期5卷 1–30页

作者： Aguirre, Alejandro Barthe, Gilles Gaboardi, Marco Garg, Deepak Katsumata, Shin-ya Sato, Tetsuya Univ Politecn Madrid Madrid Spain Aarhus Univ Aarhus Denmark MPI SP Bochum Spain IMDEA Software Inst Madrid Spain Boston Univ Boston MA 02215 USA Max Planck Inst Software Syst Saarland Informat Campus Saarbrucken Germany Natl Inst Informat Chiyoda Ku 2-1-2 Hitotsubashi Tokyo 1018430 Japan Tokyo Inst Technol Tokyo Japan

Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several domains, including security, privacy and machine learning. In this paper, we develop program logics for reasoning about adversarial computations in a higher-order setting. Our logics are built on top of a simply typed lambda-calculus extended with a graded monad for probabilities and state. The grading is used to model and restrict the memory footprint and the cost (in terms of oracle calls) of computations. Under this view, an adversary is a higher-order expression that expects as arguments the code of its oracles. We develop unary program logics for reasoning about error probabilities and expected values, and a relational logic for reasoning about coupling-based properties. All logics feature rules for adversarial computations, and yield guarantees that are valid for all adversaries that satisfy a fixed resource policy. We prove the soundness of the logics in the category of quasi-Borel spaces, using a general notion of graded predicate liftings, and we use logical relations over graded predicate liftings to establish the soundness of proof rules for adversaries. We illustrate the working of our logics with simple but illustrative examples.

关键词： probabilistic programming semantic models program logics

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Aggregators' Optimal Bidding Strategy in Sequential Day-Ahead and Intraday Electricity Spot Markets

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ENERGIES 2017年第4期10卷 450页

作者： Ayon, Xiaolin Angeles Moreno, Maria Usaola, Julio Univ Carlos III Madrid Dept Elect Engn Ave Univ 30 Madrid 28911 Spain

This paper proposes a probabilistic optimization method that produces optimal bidding curves to be submitted by an aggregator to the day-ahead electricity market and the intraday market, considering the flexible demand of his customers (based in time dependent resources such as batteries and shiftable demand) and taking into account the possible imbalance costs as well as the uncertainty of forecasts (market prices, demand, and renewable energy sources (RES) generation). The optimization strategy aims to minimize the total cost of the traded energy over a whole day, taking into account the intertemporal constraints. The proposed formulation leads to the solution of different linear optimization problems, following the natural temporal sequence of electricity spot markets. Intertemporal constraints regarding time dependent resources are fulfilled through a scheduling process performed after the day-ahead market clearing. Each of the different problems is of moderate dimension and requires short computation times. The benefits of the proposed strategy are assessed comparing the payments done by an aggregator over a sample period of one year following different deterministic and probabilistic strategies. Results show that probabilistic strategy reports better benefits for aggregators participating in power markets.

关键词： aggregator optimal bidding electricity markets probabilistic programming

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Conditional Independence by Typing

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ACM TRANSACTIONS ON programming LANGUAGES AND SYSTEMS 2022年第1期44卷 4-4页

作者： Gorinova, Maria, I Gordon, Andrew D. Sutton, Charles Vakar, Matthijs Univ Edinburgh Edinburgh Midlothian Scotland Microsoft Res Cambridge England Univ Utrecht Utrecht Netherlands

A central goal of probabilistic programming languages (PPLs) is to separate modelling from inference. However, this goal is hard to achieve in practice. Users are often forced to re-write their models to improve efficiency of inference or meet restrictions imposed by the PPL. Conditional independence (CI) relationships among parameters are a crucial aspect of probabilistic models that capture a qualitative summary of the specified model and can facilitate more efficient inference. We present an information flow type system for probabilistic programming that captures conditional independence (CI) relationships and show that, for a well-typed program in our system, the distribution it implements is guaranteed to have certain CI-relationships. Further, by using type inference, we can statically deduce which CI-properties are present in a specified model. As a practical application, we consider the problem of how to perform inference on models with mixed discrete and continuous parameters. Inference on such models is challenging in many existing PPLs, but can be improved through a workaround, where the discrete parameters are used implicitly, at the expense of manual model re-writing. We present a source-to-source semantics-preserving transformation, which uses our CI-type system to automate this workaround by eliminating the discrete parameters from a probabilistic program. The resulting program can be seen as a hybrid inference algorithm on the original program, where continuous parameters can be drawn using efficient gradient-based inference methods, while the discrete parameters are inferred using variable elimination. We implement our CI-type system and its example application in SlicStan: a compositional variant of Stan.(1)

关键词： probabilistic programming information flow types static analysis conditional independence compiler correctness

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PλωNK: Functional probabilistic NetKAT

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2020年第POPL期4卷 1–27页

作者： Vandenbroucke, Alexander Schrijvers, Tom Katholieke Univ Leuven Celestijnenlaan 200 A B-3001 Leuven Belgium

This work presents P lambda omega NK, a functional probabilistic network programming language that extends probabilistic NetKAT (PNK). Like PNK, it enables probabilistic modelling of network behaviour, by providing probabilistic choice and infinite iteration (to simulate looping network packets). Yet, unlike PNK, it also offers abstraction and higher-order functions to make programming much more convenient. The formalisation of P lambda omega NK is challenging for two reasons: Firstly, network programming induces multiple side effects (in particular, parallelism and probabilistic choice) which need to be carefully controlled in a functional setting. Our system uses an explicit syntax for thunks and sequencing which makes the interplay of these effects explicit. Secondly, measure theory, the standard domain for formalisations of (continuous) probablistic languages, does not admit higher-order functions. We address this by leveraging omega-Quasi Borel Spaces (omega QBSes), a recent advancement in the domain theory of probabilistic programming languages. We believe that our work is not only useful for bringing abstraction to PNK, but that-as part of our contribution-we have developed the meta-theory for a probabilistic language that combines advanced features like higher-order functions, iteration and parallelism, which may inform similar meta-theoretic efforts.

关键词： probabilistic programming Network Modelling Quasi-Borel Spaces omega-QBS NetKAT

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Optimal Maintenance for a System with probabilistic Time Constraint

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Safety and Reliability 2012年第3期32卷 51-59页

In this paper, we repair an optimum number of components in a system, repair time taken as a random variable in the constraint function. By applying probabilistic programming, constraints function is converted into an equivalent deterministic form. A numerical example is presented to illustrate the computational procedure for random time constraints, and the problem is solved by using LINGO software.

关键词： Selective maintenance reliability chance constraint probabilistic programming

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On Continuation-Passing Transformations and Expected Cost Analysis

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2021年第ICFP期5卷 1–30页

作者： Avanzini, Martin Barthe, Gilles Dal Lago, Ugo Inria Sophia Antipolis Mediterranee Biot France Max Planck Inst Secur & Privacy Bochum Germany Univ Bologna Bologna Italy

We define a continuation-passing style (CPS) translation for a typed lambda-calculus with probabilistic choice, unbounded recursion, and a tick operator D for modeling cost. The target language is a (non-probabilistic) lambda-calculus, enriched with a type of extended positive reals and a fixpoint operator. We then show that applying the CPS transform of an expression M to the continuation lambda(nu).0 yields the expected cost of M. We also introduce a formal system for higher-order logic, called EHOL, prove it sound, and show it can derive tight upper bounds on the expected cost of classic examples, including Coupon Collector and Random Walk. Moreover, we relate our translation to Kaminski et al.'s ert-calculus, showing that the latter can be recovered by applying our CPS translation to (a generalization of) the classic embedding of imperative programs into lambda-calculus. Finally, we prove that the CPS transform of an expression can also be used to compute pre-expectations and to reason about almost sure termination.

关键词： cost analysis probabilistic programming CPS transformation

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A Denotational Semantics for Low-Level probabilistic Programs with Nondeterminism

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Electronic Notes in Theoretical Computer Science 2019年 347卷 303-324页

作者： Di Wang Jan Hoffmann Thomas Reps Carnegie Mellon University University of Wisconsin GrammaTech Inc

probabilistic programming is an increasingly popular formalism for modeling randomness and uncertainty. Designing semantic models for probabilistic programs has been extensively studied, but is technically challenging. Particular complications arise when trying to account for (i) unstructured control-flow, a natural feature in low-level imperative programs; (ii) general recursion, an extensively used programming paradigm; and (iii) nondeterminism, which is often used to represent adversarial actions in probabilistic models, and to support refinement-based development. This paper presents a denotational-semantics framework that supports the three features mentioned above, while allowing nondeterminism to be handled in different ways. To support both probabilistic choice and nondeterministic choice, the semantics is given over control-flow hyper -graphs. The semantics follows an algebraic approach: it can be instantiated in different ways as long as certain algebraic properties hold. In particular, the semantics can be instantiated to support nondeterminism among either program states or state transformers . We develop a new formalization of nondeterminism based on powerdomains over sub-probability kernels . Semantic objects in the powerdomain enjoy a notion we call generalized convexity , which is a generalization of convexity. As an application, the paper sketches an algebraic framework for static analysis of probabilistic programs, which has been proposed in a companion paper.

关键词： probabilistic programming denotational semantics control-flow hyper-graphs nondeterminism powerdomains

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VPHL: A Verified Partial-Correctness Logic for probabilistic Programs

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ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 2015年 319卷 351-367页

作者： Rand, Robert Zdancewic, Steve Univ Penn Comp & Informat Sci Philadelphia PA 19104 USA

We introduce a Hoare-style logic for probabilistic programs, called VPHL, that has been formally verified in the Coq proof assistant. VPHL features propositional, rather than additive, assertions and a simple set of rules for reasoning about these assertions using the standard axioms of probability theory. VPHL's assertions are partial correctness assertions, meaning that their conclusions are dependent upon (deterministic) program termination. The underlying simple probabilistic imperative language, PrImp, includes a probabilistic toss operator, probabilistic guards and potentially-non-terminating while loops.

关键词： Hoare Logic Formal Verification Coq probabilistic programming Non-termination

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A Generative probabilistic Model for Leaning Complex Visual Stimuli

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Procedia Computer Science 2016年 88卷 58-63页

作者： Alexey Potapov Vita Batishcheva Department of Computer Photonics and Videomatics ITMO University St. Petersburg Russia Faculty of Liberal Arts and Sciences St. Petersburg State University St. Petersburg Russia

The problem of representing and learning complex visual stimuli in the context of modeling the process of conditional reflex formation is considered. The generative probabilistic framework is chosen which has been recently successfully applied to cognitive modeling. A model capable of learning different visual stimuli is developed in the form of a program in Church (probabilistic programming language). NAO robot is programmed to detect visual stimuli, to point at selected stimuli in a sequence of trials, and to receive reinforcement signals for correct choices. Conducted experiments showed that the robot can learn stimuli of different types showing different decision-making behavior in a series of trial that could help arranging psychophysiological experiments.

关键词： Cognitive robotics probabilistic programming Visual stimuli Conditional reflex

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Revisiting the Links-Species Scaling Relationship in FoodWebs

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PATTERNS 2020年第7期1卷 100079页

作者： MacDonald, Arthur Andrew Meahan Banville, Francis Poisot, Timothee Univ Montreal Dept Sci Biol Montreal PQ H2V 0B3 Canada Quebec Ctr Biodivers Sci Montreal PQ H3A 1B1 Canada

Predicting the number of interactions among species in a food web is an important task. These trophic interactions underlie many ecological and evolutionary processes, ranging from biomass fluxes, ecosystem stability, resilience to extinction, and resistance against novel species. We investigate and compare several ways to predict the number of interactions in food webs. We conclude that a simple beta-binomialmodel outperforms other models, with the added desirable property of respecting biological constraints. We show how this simple relationship gives rise to a predicted distribution of several quantities related to link number in food webs, including the scaling of network structure with space and the probability that a network will be stable.

关键词： DSML 2: Proof-of-Concept : Data science output has been formulated, implemented, and tested for one domain/problem food webs constant connectance link-species scaling power law probabilistic programming Bayesian methods

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