Stochastic optimization with structured distributions: The case of Bayesian nets

Abstract

In this paper, the authors consider interworking between statistical procedures for recoveringthe distribution of random parameters from observations and stochastic programmingtechniques, in particular stochastic gradient (quasigradient) methods. The proposed problemformulation is based upon a class of statistical models known as Bayesian nets. The reasonfor the latter choice is that Bayesian nets are powerful and general statistical models emergedrecently within the more general framework of Bayesian statistics, which is specificallydesigned for cases when the vector of random parameters can have considerable dimensionandyor it is difficult to come up with traditional parametric models of the joint distribution ofrandom parameters. We define the optimization problem on a Bayesian net. For the solutionof this problem, we develop algorithms for sensitivity analysis of such a net and presentcombined optimization and sampling techniques.