Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Section: New Results

Static Analysis of Probabilistic Programming Languages

Towards the verification of semantic assumptions required by probabilistic inference algorithms

Participants : Wonyeol Lee, Hangyeol Wu, Xavier Rival [correspondant] , Hongseok Yang.

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. We analysed 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 expressed what this algorithm does on models denoted by programs, and exposed 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 found a bug in one of these cases, and revealed a non-standard use of an inference engine in another, and showed that the assumptions are met in the remaining six cases.

This work has been published in [12].