Community Detection: Exact Inference with Latent Variables in an Arbitrary Domain
Abstract: We analyze the necessary and sufficient conditions for exact inference in a latent model for community detection. In latent models, each entity is associated with a latent variable following some probability distribution. The challenging question we try to solve is: can we perform exact inference without observing or estimating the latent variables, even without knowing what the domain of the latent variables is? We show that exact inference can be achieved using a semidefinite programming (SDP) approach without knowing either the latent variables or their domain. Our analysis predicts the experimental correctness of SDP with high accuracy, showing the suitability of our focus on the Karush-Kuhn-Tucker conditions and the spectrum of a properly defined matrix. Running on a laptop equivalent, our method can achieve exact inference in models with over 10000 entities efficiently. As a byproduct of our analysis, we also provide concentration inequalities with dependence on latent variables, both for bounded moment generating functions as well as for the spectra of matrices. To the best of our knowledge, these results are novel and could be useful for many other problems.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=1R7spWLnpR
Changes Since Last Submission: We made all the changes in the manuscript, from relevant comments brought up in this review and the previous review. (Removed text is in struckthrough red, added text is in blue.) Comments that were not relevant were addressed in this review and the previous review, but not changed in the manuscript.
Assigned Action Editor: ~Bryon_Aragam1
Submission Number: 2341
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