nucleation

LIT-1553: Mixed Membership Stochastic Blockmodels

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Properties5
StatusActive — read 2026-10-26 (NOTE-1179) in full, from the typeset JMLR copy; worth reading for the mixed membership stochastic blockmodel, in which a node takes one block per interaction drawn from its own membership vector, for the variational EM that fits it, and as the relational baseline a model of members' perspectives must beat. Read it knowing that its §5 claim that the blockmodel and the memberships do not compete is asserted and fails for the likelihood given memberships, that its sparsity parameter is confounded with the blockmodel's scale and its printed estimator is the fraction of zeros (THEORY-993), that K is chosen by criterion, that it cannot generate hubs, and that its protein-function check is against a weak baseline (THEORY-1008, Proposed).
Version2
Tagsnetwork-science, probabilistic-modeling
Cited as “paper” byNOTE-1179 — Airoldi, Blei, Fienberg and Xing — Mixed membership stochastic blockmodels
Cited as “source” byTHEORY-1008 — Mixed memberships fitted by a fifteen-block MMSB to 871 yeast proteins' curated physical interactions carry information about the proteins' top-level MIPS functions beyond what the functions' base rates give: after mapping blocks to functions on 87 proteins, thresholded memberships predicted the other proteins' annotations with about 87% accuracy, against about 70% for random guessing at the right proportions, THEORY-993 — In the mixed membership stochastic blockmodel the probability of an edge from p to q, given the memberships, is (1 − ρ)π_pᵀBπ_q, so the graph's likelihood given the memberships is unchanged by π ↦ Rπ, B ↦ R⁻ᵀBR⁻¹ for any invertible R that keeps the memberships on the simplex and B in [0, 1], a continuum around any solution with B's rates strictly between 0 and 1; and the sparsity parameter ρ enters only through (1 − ρ)B, so it is fixed by nothing but the bound B ≤ 1, and the paper's printed estimator of it is the fraction of absent edges whatever the fit

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Airoldi, E. M., Blei, D. M., Fienberg, S. E. & Xing, E. P. (2008). Mixed membership stochastic blockmodels. Journal of Machine Learning Research 9: 1981–2014. arXiv:0705.4485.

Read in full on 2026-10-26 from the typeset JMLR copy (NOTE-1179). The summary is checked against the reading.

Why this is here

Cited at T21 for the relational component of the reply’s combined model: members occupying several latent roles in their interactions. The record held no blockmodel. It bears on QUESTION-276, whose last clause asks whether inferred higher-level structure predicts responses to interventions beyond what the communication and authority graph already gives; a mixed-membership blockmodel of that graph is the baseline such inference must beat.

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