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Abstract:
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While many multiple graph inference methodologies operate under the implicit assumption that an explicit vertex correspondence is known across the vertex sets of the graphs, in practice these correspondences may only be partially or errorfully known. Adopting an information theoretic approach, we study the theoretical and practical impact that errorfully observed vertex correspondences can have on subsequent inference, with examples from two sample graph hypothesis testing and joint graph clustering. We then demonstrate the capacity of graph matching methodologies to recover the lost vertex alignment and, subsequently, the lost inferential performance.
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