Apparaît dans la collection : French Spring School in Theoretical Computer Science / École de Printemps d'Informatique Théorique
Probabilistic inference engines lie at the core of probabilistic programming languages. However, their correctness depends on complex mathematical properties, that many probabilistic models do not satisfy. In this lecture, we will consider a family of inference engines based on variational inference and study properties required to ensure their correctness. After describing stochastic variational inference (SVI) and showing a few common pitfalls, we will set up a static analysis approach based on a rigorous study of the semantics of the inference engine. We will identify several key semantic properties of probabilistic models and show how they can be computed statically using abstract interpretation-based static analysis. Semantic properties under consideration will include consistency of distribution sampling and various smoothness properties.To address the static analysis part, we will introduce all required background in semantics, abstract interpretation and static analysis.