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LIT-1537: Hierarchical Beta Processes and the Indian Buffet Process

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StatusActive — read 2026-10-26 (NOTE-1171) in full, from PMLR's own PDF; worth reading for the beta process as the IBP's de Finetti measure, with the predictive and the count of distinct features that follow (THEORY-985), and for the hierarchical beta process, the established way for groups to share one feature library at group-specific prevalences (THEORY-1015). Read it knowing that conjugacy is cited rather than proved, that its groups are disjoint and static, that its one experiment is a single text-classification split, and that its stated reason for a small group concentration reads against its own (9).
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Tagsprobabilistic-modeling, mathematical-statistics
Cited as “paper” byNOTE-1171 — Thibaux and Jordan — Hierarchical beta processes and the Indian buffet process
Cited as “source” byTHEORY-1015 — Groups of objects drawn from beta processes share features only if the measure they are drawn around is discrete; in the hierarchical beta process that measure is itself a beta process draw, and at each shared feature a group's prevalence is Beta(c_j b, c_j(1 − b)) around the shared prevalence b, so a small c_j lets groups differ and a large one pulls them together, THEORY-985 — The beta process BP(c, B0) is the de Finetti mixing measure of the Indian buffet process: given n objects, the next has each existing feature with probability equal to the number holding it over c + n and a Poisson(cγ/(c + n)) number of new ones, so n objects hold Poisson(γ Σ_{i<n} c/(c + i)) distinct features, which is the IBP's αH_n at c = 1 and γ = α, and c alone sets how much objects share

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Thibaux, R. & Jordan, M. I. (2007). Hierarchical beta processes and the Indian buffet process. In Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2: 564–571. https://proceedings.mlr.press/v2/thibaux07a.html.

Read 2026-10-26 in full, in NOTE-1171. The summary was checked against the reading and holds.

Why this is here

Cited at T22 and T23 as the established way for teams to share a feature library at team-specific prevalences, the alternative to the team-level structure that T23’s model writes by hand. It bears on CASE-165 and on QUESTION-276.

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