Supervised hypergraph labeling

We address the problem of labeling individual datapoints given some knowledge about (small) subsets or groups of them. The knowledge we have for a group is the likelihood value for each group member to satisfy a certain model. This problem is equivalent to hypergraph labeling problem where each datapoint corresponds to a node and the each subset correspond to a hyperedge with likelihood value as its weight. We propose a novel method to model the label dependence using an Undirected Graphical Model and reduce the problem of hypergraph labeling into an inference problem. This paper describes the structure and necessary components of such model and proposes useful cost functions. We discuss the behavior of proposed algorithm with different forms of the cost functions, identify suitable algorithms for inference and analyze required properties when it is theoretically guaranteed to have exact solution. Examples of several real world problems are shown as applications of the proposed method.