Abstract:
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Gaussian graphical model (GGM) is widely used to reflect the relationship between a large number of random variables. In this work, we generalize the classical GGM, so that each node in the graph represents a random vector instead of random variable. We propose to estimate the high-level conditional independence graph using nodewise regression. The response is one node and covariates are all other nodes, so in our setting, this regression has multivariate response and grouped covariates. The edges are decided by the block-wise sparsity of the coefficients, so we use a block-norm regularization to induce the sparsity we want. The success of graph estimation relies on the sparsity recovery of each regression, and our theory reveals under what conditions do we have exact and partial sparsity recovery for this type of regression.
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