Some Advances in Statistical modeling of Brain Structural Connectomes

It has become routine in neuroscience studies to measure brain networks for different individuals using neuroimaging. These networks are typically expressed as adjacency matrices, with each cell containing a summary of connectivity between a pair of brain regions. There is an emerging statistical literature describing methods for the analysis of such multi-network data in which nodes are common across networks but the edges vary.

There has been essentially no consideration of the important problem of outlier detection in the structural connectomics literature. In particular, for certain subjects, the neuroimaging data are so poor quality that the network cannot be reliably reconstructed. For such subjects, the resulting adjacency matrix may be mostly zero or exhibit a bizarre pattern not consistent with a functioning brain. These outlying networks may serve as influential points, contaminating subsequent statistical analyses. In chapter 2, we propose a simple Outlier DetectIon for Networks (ODIN) method relying on an influence measure under a hierarchical generalized linear model for the adjacency matrices. An efficient computational algorithm is described, and ODIN is illustrated through simulations and an application to data from the UK Biobank.

Another problem in statistical modeling of brain networks is that in the aforementioned framework based on dividing the brain into regions, the choice of regions is highly subjective and often analyses are sensitive to the way these regions are chosen. Alternative methods which do not depend on choosing such regions are computationally expensive. In chapter 3, we propose a simple but computationally efficient method based on density estimation using Ensembles of MOndrian processes(EMO). We showed our method has strong theoretical properties and is computationally fast in real world scenarios. In chapter 4, we proposed a simple way of extending the method in chapter 3 to a case where we simutaneously estimate several densities for several subjects.