Constraints and Probabilistic Networks: A Look At The Interface

Abstract

I am going to discuss the interface between two types of networks; one deterministic and one probabilistic. The deterministic network, also known as constraint network, a CSP problem, or a SAT formula, represents a collection of constraints among groups of variables.

The probabilistic network is a more organized object, represents a restricted collection of probabilistic relationships among groups of variables. These two paradigms were developed separately in the past 20–30 years and are relatively mature by now, with each paradigm equipped with its own concepts, techniques, heuristics and shortcuts. For example the concept of constraint propagation is unheard of in the probabilistic community. Similarly, notions such as sampling and Monte Carlo simulation (with guaranteed convergence) are rarely examined in constraint processing.

I will start by highlighting conceptual commonalities and differences between the two frameworks, and will propose a simple hybrid framework. I will then talk about benefits that can be obtained by importing techniques from constraint networks to probabilistic networks and back. Finally, if time permits, I will discuss how sampling techniques used in probabilistic networks can inspire algorithms for sampling solution in constraint satisfaction problems.