A decomposition strategy for the variational inference of complex systems

The drawback of these methods is that they can be computationally prohibitive especially when complex models are analyzed. In such cases, variational methods may provide an efficient and attractive alternative.

However, the variational methods reported to date are applicable to relatively simple models and most are based on a factorized approximation to the posterior distribution. Here, we propose a variational approach that is capable of handling models that consist of a system of differential-algebraic equations and whose posterior approximation can be represented by a multivariate distribution. Under the proposed approach, the solution of the variational inference problem is decomposed into three steps: a Maximum A Posteriori optimization which is facilitated by using an orthogonal collocation approach, a Preprocessing step which is based on the estimation of the eigenvectors of the posterior covariance matrix, and an Expected Propagation optimization problem.