  Hybrid continuous-discrete models naturally represent many real-world
applications in robotics, finance, and environmental engineering. Inference
with large-scale models is challenging because relational structures
deteriorate rapidly during inference with observations. The main contribution
of this paper is an efficient relational variational inference algorithm that
factors largescale probability models into simpler variational models, composed
of mixtures of iid (Bernoulli) random variables. The algorithm takes
probability relational models of largescale hybrid systems and converts them to
a close-to-optimal variational models. Then, it efficiently calculates marginal
probabilities on the variational models by using a latent (or lifted) variable
elimination or a lifted stochastic sampling. This inference is unique because
it maintains the relational structure upon individual observations and during
inference steps.
