Probabilistic programming languages allow a modeler to build probabilistic models using complex data structures with all the power of a programming language. We present CTPPL, an expressive probabilistic programming language for dynamic processes that models processes using continuous time. Time is a first class element in our language; the amount of time taken by a subprocess can be specified using the full power of the language. We show through examples that CTPPL can easily represent existing continuous time frameworks and makes it easy to represent new ones. We present semantics for CTPPL in terms of a probability measure over trajectories. We present a particle filtering algorithm for the language that works for a large and useful class of CTPPL programs.
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in parallel (and possibly interacting) have summed time-evolution operators. From this foundation, algorithms for simulation, inference and model reduction may be systematically derived. The useful consequences are potentially far-reaching in computational science, machine learning and beyond. Hybrid compositional stochastic modeling/probabilistic programming approaches may also be possible.
Yet one of the current hurdles towards developing model-based reactive systems is the number of methodsimultaneously employed, and their corresponding melange of programming and modeling languages. This paper offers an important step towards unification of reactive and model-based programming, providing the capability to monitor mixed hardware/software systems. We introduce RMPL, a rich modeling language that combines probabilistic, constraint-based modeling with reactive programming constructs, while offering a simple semantics in terms of hidden state Markov processes. We introduce probabilistic, hierarchical constraint automata, which allow Markov processes to be expressed in a compact representation that preserves the modularity of RMPL programs. Finally, a model-based executive, called RBurton is described that exploits this compact encoding to perform efficent simulation, belief state update and control sequence generation.
Michels, Steffen (Radboud University Nijmegen) | Hommersom, Arjen (Radboud University Nijmegen) | Lucas, Peter (Radboud University Nijmegen) | Velikova, Marina (Radboud University Nijmegen) | Koopman, Pieter (Radboud University Nijmegen)
Probabilistic logics combine the expressive power of logic with the ability to reason with uncertainty. Several probabilistic logic languages have been proposed in the past, each of them with their own features. In this paper, we propose a new probabilistic constraint logic programming language, which combines constraint logic programming with probabilistic reasoning. The language supports modeling of discrete as well as continuous probability distributions by expressing constraints on random variables. We introduce the declarative semantics of this language, present an exact inference algorithm to derive bounds on the joint probability distributions consistent with the specified constraints, and give experimental results. The results obtained are encouraging, indicating that inference in our language is feasible for solving challenging problems.