A characterization of product-form exchangeable feature probability functions

Battiston, Marco and Favaro, Stefano and Roy, Daniel M. and Teh, Yee Whye (2018) A characterization of product-form exchangeable feature probability functions. Annals of Applied Probability, 28 (3). pp. 1423-1448. ISSN 1050-5164

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Abstract

We characterize the class of exchangeable feature allocations assigning probability Vn,k∏kl=1WmlUn−ml to a feature allocation of n individuals, displaying k features with counts (m1,…,mk) for these features. Each element of this class is parametrized by a countable matrix V and two sequences U and W of nonnegative weights. Moreover, a consistency condition is imposed to guarantee that the distribution for feature allocations of (n−1) individuals is recovered from that of n individuals, when the last individual is integrated out. We prove that the only members of this class satisfying the consistency condition are mixtures of three-parameter Indian buffet Processes over the mass parameter γ, mixtures of N-dimensional Beta–Bernoulli models over the dimension N, or degenerate limits thereof. Hence, we provide a characterization of these two models as the only consistent exchangeable feature allocations having the required product form, up to randomization of the parameters.

Item Type:
Journal Article
Journal or Publication Title:
Annals of Applied Probability
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1800/1804
Subjects:
ID Code:
132140
Deposited By:
Deposited On:
21 Mar 2019 16:20
Refereed?:
Yes
Published?:
Published
Last Modified:
20 May 2020 07:15