|
Abstract:
|
We propose the combinatorial inference to explore the topological structures of graphical models. The combinatorial inference can conduct the hypothesis tests on many graph properties including connectivity, hub detection, perfect matching, etc. In particular, our methods can be applied to any graph property which is invariant under the addition of edges. On the other side, we also propose a shortest self-returning path lemma to prove the general optimality of our testing procedures for various graph properties. The combinatorial inference is also generalized to the time-varying graphical models and we can infer the dynamic topological structures for graphs. Our methods are applied to the neuroscience by discovering hub voxels contributing to visual memories (Joint work with Junwei Lu, Matey Neykov, Kean Ming Tan).
|
