Stochastic optimization with structured distributions: The case of Bayesian nets

In this paper, the authors consider interworking between statistical procedures for recovering the distribution of random parameters from observations and stochastic programming techniques, in particular stochastic gradient (quasigradient) methods. The proposed problem formulation is based upon a class of statistical models known as Bayesian nets. The reason for the latter choice is that Bayesian nets are powerful and general statistical models that emerged recently within the more general framework of Bayesian statistics, which is specifically designed for cases when the vector of random parameters can have considerable dimension and/or it is difficult to come up with traditional parametric models of the joint distribution of random parameters. We define the optimization problem on a Bayesian net. For the solution of this problem, we develop algorithms for sensitivity analysis of such a net and present combined optimization and sampling techniques.