Structured Prediction of Degree Constrained Subgraphs
نویسندگان
چکیده
Recent study of complex graphs has revealed that not all of them are made equal. Man-made and naturally-formed graphs exhibit structural regularity and have common degree distributions that differ a great deal from the random graphs of Erdos-Renyi. A coincident discovery, made in the machine learning community, is that several multivariate prediction problems can be solved with greater accuracy via structural dependencies imposed on the outputs; structured prediction. In other words, not all outputs are made equal. In this paper, we develop machine learning algorithms to enable the prediction of naturally structured graphs, a problem we call structured graph inference. Given partially observed connectivity over n observed objects, return a complementary set of directed edges connecting the objects together into a graph while satisfying topological constraints. Our model learns to predict connectivity of ordered pairs of objects within a structured prediction framework to enforce in-degree and out-degree conditions, while current methods for graph inference largely ignore global characteristics of graphs. If no connectivity constraints can be specified a priori, the model learns to predict these from the observed component of the graph. This specializes independent link prediction and relational learning to interdependent prediction of edges within a combinatorial family of graphs. We demonstrate the characteristics of the model as it learns to predict 2-dimensional geometric graphs, and subsequently analyze its performance on several structured graphs including protein-protein interation, social network and citation network graphs.
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