Variational Bayes Inference for Generalized Associative Functional Networks

We propose a Bayesian framework for generalized associative functional networks (GAFN) and provide variational Bayes (VB) learning algorithm to approximate the posterior distributions over parameters of GAFN. The learning procedure for GAFN involves equality constraints on parameters, thus conventional approaches, like probabilistic graphical model or Lagrange multiplier method, will be inconvenient or expensive for solving the GAFN model in a direct way. We provide a linear transformation algorithm for the learning of parameters of GAFN. By means of the linear transformation, the evaluation of Lagrange multipliers is avoided and an iterative VB approximate procedure is restricted to a subspace of the original weight space. The VB framework naturally prevents overfltting and statistical inference can be made conveniently for weights of GAFN by the approximate posterior distributions over weights. The Bayesian GAFN is applied to autoregressive time series and the experimental results are comparable to other existing methods.