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A characterization of product-form exchangeable feature probability functions

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A characterization of product-form exchangeable feature probability functions. / Battiston, Marco; Favaro, Stefano; Roy, Daniel M. et al.
In: Annals of Applied Probability, Vol. 28, No. 3, 01.06.2018, p. 1423-1448.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Battiston, M, Favaro, S, Roy, DM & Teh, YW 2018, 'A characterization of product-form exchangeable feature probability functions', Annals of Applied Probability, vol. 28, no. 3, pp. 1423-1448. https://doi.org/10.1214/17-AAP1333

APA

Battiston, M., Favaro, S., Roy, D. M., & Teh, Y. W. (2018). A characterization of product-form exchangeable feature probability functions. Annals of Applied Probability, 28(3), 1423-1448. https://doi.org/10.1214/17-AAP1333

Vancouver

Battiston M, Favaro S, Roy DM, Teh YW. A characterization of product-form exchangeable feature probability functions. Annals of Applied Probability. 2018 Jun 1;28(3):1423-1448. doi: 10.1214/17-AAP1333

Author

Battiston, Marco ; Favaro, Stefano ; Roy, Daniel M. et al. / A characterization of product-form exchangeable feature probability functions. In: Annals of Applied Probability. 2018 ; Vol. 28, No. 3. pp. 1423-1448.

Bibtex

@article{3b657c5b744c42a18f01481418c22ed0,
title = "A characterization of product-form exchangeable feature probability functions",
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.",
keywords = "Indian buffet process, exchangeable feature allocations, Gibbs-type partitions",
author = "Marco Battiston and Stefano Favaro and Roy, {Daniel M.} and Teh, {Yee Whye}",
year = "2018",
month = jun,
day = "1",
doi = "10.1214/17-AAP1333",
language = "English",
volume = "28",
pages = "1423--1448",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "3",

}

RIS

TY - JOUR

T1 - A characterization of product-form exchangeable feature probability functions

AU - Battiston, Marco

AU - Favaro, Stefano

AU - Roy, Daniel M.

AU - Teh, Yee Whye

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - Indian buffet process

KW - exchangeable feature allocations

KW - Gibbs-type partitions

U2 - 10.1214/17-AAP1333

DO - 10.1214/17-AAP1333

M3 - Journal article

VL - 28

SP - 1423

EP - 1448

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 3

ER -