Concentration in the Generalized Chinese Restaurant Process

R. I. Oliveira (), Alfredo Pereira and R. Ribeiro ()
Additional contact information
R. I. Oliveira: IMPA
R. Ribeiro: PUC Chile

Sankhya A: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 10, 628-670

Abstract: Abstract The Generalized Chinese Restaurant Process (GCRP) describes a sequence of exchangeable random partitions of the numbers { 1 , … , n } $\{1,\dots ,n\}$ . This process is related to the Ewens sampling model in Genetics and to Bayesian nonparametric methods such as topic models. In this paper, we study the GCRP in a regime where the number of parts grows like nα with α > 0. We prove a non-asymptotic concentration result for the number of parts of size k = o ( n α / ( 2 α + 4 ) / ( log n ) 1 / ( 2 + α ) ) $k=o(n^{\alpha /(2\alpha +4)}/(\log n)^{1/(2+\alpha )})$ . In particular, we show that these random variables concentrate around ckV∗nα where V∗nα is the asymptotic number of parts and ck ≈ k−(1+α) is a positive value depending on k. We also obtain finite-n bounds for the total number of parts. Our theorems complement asymptotic statements by Pitman and more recent results on large and moderate deviations by Favaro, Feng and Gao.

Keywords: Random partition; generalized chinese restaurant process; concentration inequality.; Primary 60F10; Secondary 62E20 (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s13171-020-00210-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00210-7

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-020-00210-7

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().