Sparse Bipartite Graphs: Concentration, Regularization and Applications
DescriptionNetwork analysis has become a popular research area over the past few years, with applications and contributions from many disciplines including statistics, computer science, social sciences, physics and biology. Bipartite graphs are popular data in many fields, such as recommendation system, statistical physics, proteomic parsimony. In this project, we propose to study a fundamental concentration inequality on bipartite graphs, then apply the theoretical result to a series of statistical models, with application to various fields.The random matrix theory on unipartite networks has been well studied, but the application of the existing results on bipartite graphs usually gives suboptimal results. Therefore, we will develop some fundamental concentration inequalities on random bipartite graphs. Our proving skills will based on classical techniques on sparse random graph and recent development in Hanson-Wright inequality.Furthermore, we will apply the concentration inequality for random bipartite graphs on statistical learning in bipartite networks. We will focus on subspace estimation, Bernoulli mixture models and stochastic block models. Our goal is to obtain optimal error rates using appropriate algorithms for different tasks.
|Effective start/end date||1/01/22 → …|