Abstract:
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We propose a novel inferential framework for estimating and uncertainty assessment of large-scale spatial graphical models with a total cardinality constraint. This work has two major contributions. (i) From a computational perspective, we need to minimize the summation of massive amounts of localized loss functions coupled by a global cardinality constraint. Though this optimization problem is highly nonconvex, we propose a dual ascent algorithm which runs in an iterative fashion. Within each iteration, the algorithm divides the global graph estimation problem into many nodewise neighborhood pursuit problems which can be trivially solved by any parallel computing architectures (e.g., GPU or cloud). Between iterations, the algorithm only needs to update a scalar dual variable and is communication-efficient. Theoretically, we show that the computational accuracy (measure by averaged duality gap) increases when the problem scale (measured by the number of nodes) increases. Thus we see a bless of massive scale. We provide a convex geometry justification of this seemingly surprising phenomenon, along with a rigorous characterization of the diminishing rate of the duality gap.
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