A CHARACTERIZATION OF PRODUCT-FORM EXCHANGEABLE FEATURE PROBABILITY FUNCTIONS
成果类型：
Article
署名作者：
Battiston, Marco; Favaro, Stefano; Roy, Daniel M.; Teh, Yee Whye
署名单位：
University of Oxford; University of Turin; University of Toronto; Collegio Carlo Alberto
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/17-AAP1333
发表日期：
2018
页码：
1423-1448
关键词：
摘要：
We characterize the class of exchangeable feature allocations assigning probability V-n,V-k Pi(l=1 WmlUn-ml)-W-k to a feature allocation of n individuals, displaying k features with counts (m(1), . . . ,m(k)) 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 gamma, 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.
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