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LIT-1556: The Indian Buffet Process: An Introduction and Review

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Properties6
StatusActive — read 2026-10-26 (NOTE-1172) in full, from JMLR's own PDF; worth reading for the derivation of the IBP as the limit of a finite beta–Bernoulli model, for K+ ~ Poisson(αH_N) and Poisson(α) features per object, and as a map of the IBP's variants to 2010, including the Markov IBP closest to a dynamic feature model. Read it knowing that αH_N is stated for the limit only and the finite model's expected count of occupied features is strictly below it (THEORY-999), that its posterior Gibbs sampler is by its own account heuristic, and that its demonstrations are single runs on data built to suit the model.
Version4
Tagsprobabilistic-modeling, mathematical-statistics
ExtendsLIT-1623 — Infinite Latent Feature Models and the Indian Buffet Process
Cited as “paper” byNOTE-1172 — Griffiths and Ghahramani — The Indian buffet process: an introduction and review
Cited as “source” byTHEORY-1043 — The finite feature model in which each of K features has prevalence Beta(α/K, 1) has, as K grows, a limit on equivalence classes of binary matrices that ignore the order of columns, and the Indian buffet process, in which the i-th object takes each earlier feature with probability m/i and Poisson(α/i) new ones, produces the same distribution, so its objects are exchangeable and the number of features they hold is Poisson(αH_N), 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, THEORY-999 — In the finite beta–Bernoulli feature model with prevalences Beta(α/K, 1), the expected number of occupied features among N objects is K(1 − (α/K)B(α/K, N + 1)), strictly below the Indian buffet process's αH_N for every finite K and tending to it as K grows, and each object holds Kα/(K + α) features on average rather than α

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Griffiths, T. L. & Ghahramani, Z. (2011). The Indian buffet process: An introduction and review. Journal of Machine Learning Research 12: 1185–1224. https://jmlr.org/papers/v12/griffiths11a.html.

Read 2026-10-26 in full, in NOTE-1172. The summary was checked against the reading and holds. What the reading adds is in THEORY-999: the αH_N count T23 quotes is the limit’s, and at T23’s K = 16 the finite model expects 6.83 occupied features.

Why this is here

Cited at T22, where the owner proposed the Indian buffet process for inferring employees’ overlapping latent features without fixing their number, and at T23, whose dynamic beta–Bernoulli model starts from an IBP prior truncated at a finite K. The record held the IBP only as the alternative Friston et al. name in NOTE-485 (LIT-615). The reply’s marginal E[K_N] = αH_N is checked in CASE-165, with where its finite and dynamic versions depart from it. It is the candidate method of QUESTION-276, and the IBP is the latent-feature prior on which CLAIM-454’s distinction turns.

Note of 2026-10-27: the Markov IBP, now held

The Markov IBP that this review’s §7.4 describes, and that the status note calls the closest variant to a dynamic feature model, was registered and read on 2026-10-27 as LIT-1577 (NOTE-1199). The review cites it as Van Gael et al., NIPS volume 21, 2009, the year of the printed volume; the conference was December 2008, and the record dates it 2008-12-01. §7.4’s description of its two per-column parameters is confirmed against it.

Note of 2026-10-27 (later): the original paper, now held

The version-1 history says the original conference paper (Griffiths and Ghahramani, NIPS 2005, “Infinite latent feature models and the Indian buffet process”) “was not cited and is not registered”. It is now registered: read on 2026-10-27, at the owner’s request (“file the next readings”), as LIT-1623 (NOTE-1208). This review is its long version, so it now extends it. The original’s limit theorem and its αH_N count are THEORY-1043; like the review, it states αH_N for the limit only and gives no finite-K count. The stick-breaking construction the review’s §7 cites as Teh et al. 2007 is LIT-1627, read the same day (THEORY-1041). That the exchange did not cite the NIPS paper remains true. The status is unchanged.

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