Cantor meets Scott: semantic foundations for probabilistic networks

Smolka, Steffen; Kumar, Praveen; Foster, Nate; Kozen, Dexter; Silva, Alexandra

doi:10.1145/3009837.3009843

Cited by 31 publications

(50 citation statements)

References 64 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Prior work on ProbNetKAT [46] gave a measure-theoretic semantics and an implementation that approximated programs using sequences of monotonically improving estimates. While these estimates were proven to converge in the limit, [46] offered no guarantees about the convergence rate. In fact, there are examples where the approximations do not converge after any finite number of steps, which is obviously undesirable in a tool.…”

Section: Related Workmentioning

confidence: 99%

“…In the original ProbNetKAT language, programs manipulate sets of packet histories-non-empty, finite sequences of packets modeling trajectories through the network [13,46]. The resulting state space is uncountable and modeling the semantics properly requires full-blown measure theory as some programs generate continuous distributions.…”

Section: A Probnetkat Denotational Semanticsmentioning

confidence: 99%

“…Proposition A.1. Let − denote the semantics defined in Smolka et al [46]. Then for all dup-free programs p and inputs a ∈ 2 Pk , we have p (a) = p (a), where we identify packets and histories of length one.…”

Section: A Probnetkat Denotational Semanticsmentioning

confidence: 99%

“…Whereas state-of-the-art tools can easily handle deterministic networks with hundreds of thousands of nodes, probabilistic tools are currently orders of magnitude behind. This paper presents McNetKAT, a new tool for reasoning about probabilistic network programs written in the guarded and history-free fragment of Probabilistic NetKAT (ProbNetKAT) [4,13,14,46]. ProbNetKAT is an expressive programming language based on Kleene Algebra with Tests, capable of modeling a variety of probabilistic behaviors and properties including randomized routing [30,48], uncertainty about demands [40], and failures [19].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Scalable verification of probabilistic networks

Smolka

Kumar

Kahn

et al. 2019

Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

Self Cite

View full text Add to dashboard Cite

This paper presents McNetKAT, a scalable tool for verifying probabilistic network programs. McNetKAT is based on a new semantics for the guarded and history-free fragment of Probabilistic NetKAT in terms of finite-state, absorbing Markov chains. This view allows the semantics of all programs to be computed exactly, enabling construction of an automatic verification tool. Domain-specific optimizations and a parallelizing backend enable McNetKAT to analyze networks with thousands of nodes, automatically reasoning about general properties such as probabilistic program equivalence and refinement, as well as networking properties such as resilience to failures. We evaluate McNetKAT's scalability using real-world topologies, compare its performance against state-of-the-art tools, and develop an extended case study on a recently proposed data center network design.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: A Probnetkat Denotational Semanticsmentioning

confidence: 99%

Section: A Probnetkat Denotational Semanticsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Scalable verification of probabilistic networks

Smolka

Kumar

Kahn

et al. 2019

Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

Self Cite

View full text Add to dashboard Cite

show abstract

“…The consequence of having random choice in a programming language has been actively investigated by the semantics researchers from the early days [Borgström et al 2016;Ehrhard et al 2014;Heunen et al 2017;Jones and Plotkin 1989;Kozen 1981;Smolka et al 2017;Staton 2017;Staton et al 2016;Toronto et al 2015;Vákár et al 2019]. Our work uses the technique developed in this endeavour, such as Giry monad and denotational formulation of idealised importance sampling [Staton et al 2016].…”

Section: Related Workmentioning

confidence: 99%

Towards verified stochastic variational inference for probabilistic programs

Lee

Rival

et al. 2019

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been explored intensely, which led to the development of so called deep probabilistic programming languages, such as Pyro, Edward and ProbTorch. At the core of this development lie inference engines based on stochastic variational inference algorithms. When asked to find information about the posterior distribution of a model written in such a language, these algorithms convert this posterior-inference query into an optimisation problem and solve it approximately by a form of gradient ascent or descent. In this paper, we analyse one of the most fundamental and versatile variational inference algorithms, called score estimator or REINFORCE, using tools from denotational semantics and program analysis. We formally express what this algorithm does on models denoted by programs, and expose implicit assumptions made by the algorithm on the models. The violation of these assumptions may lead to an undefined optimisation objective or the loss of convergence guarantee of the optimisation process. We then describe rules for proving these assumptions, which can be automated by static program analyses. Some of our rules use nontrivial facts from continuous mathematics, and let us replace requirements about integrals in the assumptions, such as integrability of functions defined in terms of programs' denotations, by conditions involving differentiation or boundedness, which are much easier to prove automatically (and manually). Following our general methodology, we have developed a static program analysis for the Pyro programming language that aims at discharging the assumption about what we call model-guide support match. Our analysis is applied to the eight representative model-guide pairs from the Pyro webpage, which include sophisticated neural network models such as AIR. It finds a bug in two of these cases, and shows that the assumptions are met in the others.In this paper, we consider inference engines that lie at the core of so called deep probabilistic programming languages, such as Pyro [Bingham et al. 2019], Edward [Tran et al. 2018, 2016 and ProbTorch [Siddharth et al. 2017]. These languages let their users freely mix deep neural networks with constructs from probabilistic programming, in particular, those for writing Bayesian probabilistic models. In so doing, they facilitate the development of probabilistic deep-network models that may address the problem of measuring the uncertainty in current non-Bayesian deepnetwork models; a non-Bayesian model may predict that the price of energy goes up and that of a house goes down, but it cannot express, for instance, that the model is very confident with the first prediction but not the second.The primary inference engines for these deep probabilistic programming languages implement stochastic variational inference algorithms. Converting infer...

show abstract

Layer by Layer – Combining Monads

Dahlqvist

Parlant

Silva

2018

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

We develop a modular method to build algebraic structures. Our approach is categorical: we describe the layers of our construct as monads, and combine them using distributive laws. Finding such laws is known to be difficult and our method identifies precise sufficient conditions for two monads to distribute. We either (i) concretely build a distributive law which then provides a monad structure to the composition of layers, or (ii) pinpoint the algebraic obstacles to the existence of a distributive law and suggest a weakening of one layer that ensures distributivity. This method can be applied to a step-by-step construction of a programming language. Our running example will involve three layers: a basic imperative language enriched first by adding non-determinism and then probabilistic choice. The first extension works seamlessly, but the second encounters an obstacle, resulting in an 'approximate' language very similar to the probabilistic network specification language ProbNetKAT.

show abstract

Cantor meets Scott: semantic foundations for probabilistic networks

Cited by 31 publications

References 64 publications

Scalable verification of probabilistic networks

Scalable verification of probabilistic networks

Towards verified stochastic variational inference for probabilistic programs

Layer by Layer – Combining Monads

Contact Info

Product

Resources

About