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LIT-1548: Dependent Indian Buffet Processes

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Properties5
StatusActive — read 2026-10-26 (NOTE-1175) in full, from PMLR's own PDF; worth reading for the thresholded-Gaussian-process construction that keeps each feature's prevalence fixed over a covariate while its covariance sets persistence, the established comparator for a dynamic latent feature model (THEORY-1006). Read it knowing that its claim of IBP marginals at every covariate value holds for the whole matrix only in its collapsed model, that features stay independent of one another, and that its evidence is two prediction comparisons with the plain IBP.
Version2
Tagsprobabilistic-modeling, mathematical-statistics
Cited as “paper” byNOTE-1175 — Williamson, Orbanz and Ghahramani — Dependent Indian buffet processes
Cited as “source” byTHEORY-1006 — In the dependent Indian buffet process each item's feature indicator is a Gaussian process thresholded at the quantile of a stick length that does not change with the covariate, so its prevalence is the same at every covariate value and its persistence is set separately by the covariance; the whole feature matrix at a covariate value is an Indian buffet process only when there is no shared feature-level process, and with one the items are correlated and fewer features are occupied, THEORY-1019 — Under the Markov Indian buffet process the expected number of features on at the first time step is α, as in the Indian buffet process, but it rises over time toward α·E[ln((2 − b)/(1 − b))] with b ~ Beta(γ, δ), which is 9.04 at γ = 10 and δ = 1, so after the first step the rows are not distributed as an Indian buffet process

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Williamson, S., Orbanz, P. & Ghahramani, Z. (2010). Dependent Indian buffet processes. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9: 924–931. https://proceedings.mlr.press/v9/williamson10a.html.

Read 2026-10-26 in full, in NOTE-1175. The summary was checked against the reading and holds.

Why this is here

Cited at T22 for perspectives becoming active, inactive or reorganized as a company changes, and at T23 as the construction its dynamic model is not. T23’s model keeps the IBP prior only at its first time step (CASE-165); this is the established model in which every item’s feature keeps the same prevalence at every covariate value, the whole allocation staying IBP-distributed in its collapsed form (THEORY-1006), and so the comparator for that case and for QUESTION-276.

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