Learning Non-Linear Functions With Factor Graphs

We show how to use a discrete-variable factor graph for learning non-linear continuous functions from examples. The paper proposes a scheme for embedding soft quantization in a probabilistic Bayesian graph. The quantized input variables are grouped into a compound variable that is mapped through a stochastic matrix into the discrete output distribution. Specific output values are then obtained through a process of de-quantization. The information flow carried by message propagation is bi-directional and an algorithm for learning the factor graph parameters is explicitly derived. The model, that can easily merge discrete and continuous variables, is demonstrated with examples and simulations.