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Contextual Stochastic Block Models
Yash Deshpande
Andrea Montanari Elchanan Mossel Subhabrata Sen
Two paradigms for clustering
Similarity-based Feature-based
Contextual Stochastic Block Models Yash Deshpande Andrea Montanari - - PowerPoint PPT Presentation
Contextual Stochastic Block Models Yash Deshpande Andrea Montanari - - PowerPoint PPT Presentation
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,
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What if we have both?
- Ecological networks: covariates on species (mass, feed,…)
- Citation networks: covariates from article (keyword, journal,…)
- …
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A statistical model
Graph similarity Gaussian mixture covariates
Two latent clusters, encoded as 𝑤 ∈ {±1}'
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Each individually
Graph similarity
Theorem (MNS13, 15, Mas14): 𝑤 recoverable from similarity graph if and only if:
Gaussian mixture covariates
Theorem (BBAP05, OMH13): 𝑤 recoverable from covariates if and only if:
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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:
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