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arXiv · 1903.10092

An Exact No Free Lunch Theorem for Community Detection

Arya D. McCarthy·Tongfei Chen·Seth Ebner
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Abstract

A precondition for a No Free Lunch theorem is evaluation with a loss function which does not assume a priori superiority of some outputs over others. A previous result for community detection by Peel et al. (2017) relies on a mismatch between the loss function and the problem domain. The loss function computes an expectation over only a subset of the universe of possible outputs; thus, it is only asymptotically appropriate with respect to the problem size. By using the correct random model for the problem domain, we provide a stronger, exact No Free Lunch theorem for community detection. The claim generalizes to other set-partitioning tasks including core/periphery separation, $k$-clustering, and graph partitioning. Finally, we review the literature of proposed evaluation functions and identify functions which (perhaps with slight modifications) are compatible with an exact No Free Lunch theorem.

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Arya D. McCarthy, Tongfei Chen, Seth Ebner. 2019-03-25. An Exact No Free Lunch Theorem for Community Detection. https://doi.org/10.1007/978-3-030-36687-2_15

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