Inference over heterogeneous finite-/infinite-dimensional systems using factor graphs and Gaussian processes

The ability to reason over partially observable networks of interacting states is a fundamental competency in probabilistic robotics. While the well-known factor graph and Gaussian process models provide flexible and computationally efficient solutions for this inference problem in the special cases in which all of the hidden states are either finite-dimensional parameters or real-valued functions, respectively, in many cases we are interested in reasoning about heterogeneous networks whose hidden states are comprised of both finite-dimensional parameters and functions. To that end, in this paper we propose a novel probabilistic generative model that incorporates both factor graphs and Gaussian processes to model these heterogeneous systems. Our model improves upon prior approaches to inference within these networks by removing the assumption of any specific set of conditional independences amongst the modeled states, thereby significantly expanding the class of systems that can be represented. Furthermore, we show that inference within this model can always be performed by means of a two-stage procedure involving inference within a factor graph followed by inference over a Gaussian process; by exploiting fast inference methods for the individual factor graph and Gaussian process models to solve each of these subproblems in succession, we thus obtain a general framework for computationally efficient inference over heterogeneous finite-/infinite-dimensional systems.