Abstract:
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Graphical models have proven useful in describing relations among interacting units. In this presentation, we will introduce graphical models to link the inverse of covariance matrix, called the precision matrix, to covariates, to locate the structural change of a graph as a function of covariates. In neuroimaging, for instance, functional connectivity of regions of interest concerns the relationship between brain activity and specific mental functions. In such a situation, the functional connectivity is described by node connectivity over a graph, with each node corresponding to one region of interest. Of particular importance is how brain connectivity responds to certain experimental conditions over subjects to facilitate population inference, where brain images of each subject are acquired under certain specific conditions. A constrained likelihood method is used for regression analysis, where sparsity and spatial constraints are imposed to estimate the graph structure through covariates. Some computational and theoretical aspects will be discussed, particularly on scaleable computation.
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