Probabilistic modeling & programming
Graphical models in probability and statistics are a core concept in the growing area of probabilistic reasoning and probabilistic programming—graphical models include Bayesian networks and factor graphs. In cooperation with Jean-Baptiste Raclet (IRIT-CNRS, Toulouse), we develop a new model of Mixed (nondeterministic/probabilistic) Automata that subsumes both nondeterministic automata and graphical probabilistic models. Mixed automata are equipped with parallel composition, simulation relation, and support message passing algorithms inherited from graphical probabilistic models. We also show how Segala and Lynch Probabilistic Automata can be mapped to Mixed Automata by preserving simulation relations. However, parallel compositions differ with most notions of Probabilistic Automata; our definition suits Probabilistic Programming.
Mixed Automata can be seen as a framework for components. In a previous work, we developed on top of Mixed Automata a specification framework called Mixed (nondeterministic/probabilistic) Interfaces. Roughly speaking, a Mixed Interface is a Mixed Automaton, whose transitions are labeled with a must or a may. A Mixed Automaton M is said to implement Mixed Interface S (we also say: is a model of) if M offers all must transitions and only may transitions of S. Mixed Interfaces are partially ordered by refinement and are equipped with a parallel composition (but no quotient). Mixed Interfaces subsume Abstract Probabilistic Automata of Delahaye et al. regarding refinement relation. They, however, differ in the way parallel composition is defined.
More information about this work in progress can be found in the following research report.