Language-Constraint Reachability Learning in Probabilistic Graphs

Probabilistic graphs model uncertainty by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. One of the main issues in probabilistic graphs is how to compute the connectivity of the network. The network reliability problem [4] is a generalization of the pairwise reachability, in which the goal is to determine the probability that all pairs of nodes are reachable from one another. Unlike a deterministic graph in which the reachability function is a binary value function indicating whether or not there is a path connecting two nodes, in the case of probabilistic graphs the function assumes probabilistic values. The concept of reachability in probabilistic graphs is used, along with its specialization, as a tool to compute how two nodes in the graph are likely to be connected. Reachability plays an important role in wide range of applications, such as in peer-to-peer networks [3, 18], for probabilistic-routing problem [2, 10], in road network [11], and in trust analysis in social networks [22].As adopted in these works, reachability is quite similar to the general concept of link prediction [9], whose task may be formalized as follows. Given a networked structure (V,E) made up of a set of data instances V and set of observed links E among some nodes in V, the task corresponds to predict how likely should exist an unobserved link between two nodes in the network. The extension to probabilistic graphs adds an important ingredient that should be adequately exploited.