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A graphical model is a structured representation of the data generatingprocess. The traditional method to reason over random variables is to performinference in this graphical model. However, in many cases the generatingprocess is only a poor approximation of the much more complex true datagenerating process, leading to suboptimal estimation. The subtleties of thegenerative process are however captured in the data itself and we can `learn toinfer', that is, learn a direct mapping from observations to explanatory latentvariables. In this work we propose a hybrid model that combines graphicalinference with a learned inverse model, which we structure as in a graph neuralnetwork, while the iterative algorithm as a whole is formulated as a recurrentneural network. By using cross-validation we can automatically balance theamount of work performed by graphical inference versus learned inference. Weapply our ideas to the Kalman filter, a Gaussian hidden Markov model for timesequences, and show, among other things, that our model can estimate thetrajectory of a noisy chaotic Lorenz Attractor much more accurately than eitherthe learned or graphical inference run in isolation.

Combining Generative and Discriminative Models for Hybrid Inference