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Abstract:
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When performing paired graph inference or inference across a time series of graphs, often one needs to know an explicit vertex correspondence across the the vertex sets of the graphs. We develop the setting and theory needed to address the following questions: (i) How much information is lost if the labeling across graphs is unknown or errorfully known? (ii) How does this information loss impact subsequent inference? (iii) Can we recover the lost information and subsequent lost inferential performance via graph matching? Lastly, we demonstrate the practical effect that graph shuffling---and subsequent matching---can have on joint graph clustering.
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