Contextual Stochastic Block Models Yash Deshpande Andrea Montanari - PowerPoint PPT Presentation

Aug 04, 2023 •226 likes •315 views

Contextual Stochastic Block Models Yash Deshpande Andrea Montanari Elchanan Mossel Subhabrata Sen Two paradigms for clustering Similarity-based Feature-based What if we have both? Ecological networks: covariates on species (mass,

Contextual Stochastic Block Models Yash Deshpande Andrea Montanari Elchanan Mossel Subhabrata Sen
Two paradigms for clustering Similarity-based Feature-based
What if we have both? • Ecological networks: covariates on species (mass, feed,…) • Citation networks: covariates from article (keyword, journal,…) • …
A statistical model Two latent clusters, encoded as 𝑤 ∈ {±1} ' Graph similarity Gaussian mixture covariates
Each individually Graph similarity Gaussian mixture covariates Theorem (MNS13, 15, Mas14): Theorem (BBAP05, OMH13): 𝑤 recoverable from similarity 𝑤 recoverable from covariates if graph if and only if: and only if:
Our result combines two phase transitions Informal theorem (D, Montanari, Mossel, Sen) In the limit of large degree 𝑒 , 𝑤 recoverable from graph and covariate data if and only if:
Thank you! Room 210, Poster # 79 5pm – 7pm

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