Bayesian networks are graphical models for representing multivariate probability distributions. Over the last decade, they have become the method of choice for the representation of uncertainty in artificial intelligence. Today, they play a crucial role in many application areas including modern expert systems, diagnosis engines, and decision support systems.
The early research in Bayesian networks focused on finding computationally efficient ways of calculating probabilities from networks designed using expert knowledge. In recent years, there has been a significant effort to develop methods and algorithms for inducing Bayesian networks directly from data. The significance of such methods is enormous as they provide a principled approach for semi-parametric density estimation, data analysis, pattern classification, and modeling.
In spite of many successful applications and interesting research, Bayesian network research is still facing grand challenges. As opposed to commonly held beliefs, model selection problem does not yet have a satisfactory solution (marginal likelihood scoring function is optimal only in a very restricted setting). Learning Bayesian networks with latent variables is hard already for tree-structured networks (also known as mixture models). It seems that for many practical instances of Bayesian networks probabilistic inference is computationally very inefficient thus underlining the NP-completeness of the inference problems. In this talk we will discuss many of the fundamental research issues in modeling with Bayesian networks, problems with the current approaches to inference and learning, and pragmatic difficulties arising in real life applications.