Random Walks on Hypergraphs with Applications to Disease-Gene Prioritization

Typically, gene interaction networks are expressed as graphs, storing pairwise interactions between genes. Because of the vast amount of literature on statistical graph inference, this is a useful representation in practice. However, such a pairwise representation ignores more complex features of gene interactions, such as gene regulation and assembly. In this thesis, we propose a hypergraph model for gene interaction networks. Since many network-based algorithms rely on random walks, we analyze our model through the viewpoint of random walks. We outline a general framework for random walks on a hypergraph, and we show in a precise sense that random walks on hypergraphs are not special cases of random walks on graphs. We also de€ne a mapping between hypergraphs and graphs, and use that mapping to build a hypergraph from an already-existing graph representation of a gene interaction network. We then use this hypergraph network to perform disease-gene prioritization via the PageRank algorithm. For monogenic diseases, we €nd that the hypergraph noticeably outperforms the graph, demonstrating the value of using hypergraphs as gene interaction networks.