  We propose a method for extracting hierarchical backbones from a bipartite
network. Our method leverages the observation that a hierarchical relationship
between two nodes in a bipartite network is often manifested as an asymmetry in
the conditional probability of observing the connections to them from the other
node set. Our method estimates both the importance and direction of the
hierarchical relationship between a pair of nodes, thereby providing a flexible
way to identify the essential part of the networks. Using semi-synthetic
benchmarks, we show that our method outperforms existing methods at identifying
planted hierarchy while offering more flexibility. Application of our method to
empirical datasets---a bipartite network of skills and individuals as well as
the network between gene products and Gene Ontology (GO) terms---demonstrates
the possibility of automatically extracting or augmenting ontology from data.
