Central limit theorems for an Indian buffet model with random weights

Abstract

The three-parameter Indian buffet process is generalized. The possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let $L_n$ be the number of dishes experimented by the first $n$ customers, and let ${\overline{K}}_n=(1/n){\sum }_{i=1}^n{K}_i$ where $K_i$ is the number of dishes tried by customer $i$. The asymptotic distributions of $L_n$ and ${\overline{K}}_n$, suitably centered and scaled, are obtained. The convergence turns out to be stable (and not only in distribution). As a particular case, the results apply to the standard (i.e., nongeneralized) Indian buffet process.

Published in at http://dx.doi.org/10.1214/14-AAP1002 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (9)

• A survey of random processes with reinforcement
• Nonparametric Bayesian sparse factor models with application to gene expression modeling
• Limit theorems for a class of identically distributed random variables
• Nonparametric Link Prediction in Dynamic Networks
• Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn
• Correlated Non-Parametric Latent Feature Models
• A Non-Parametric Bayesian Method for Inferring Hidden Causes
• The Phylogenetic Indian Buffet Process: A Non-Exchangeable Nonparametric Prior for Latent Features
• Distance Dependent Infinite Latent Feature Models

Cited by in corpus (4)

• More for less: Predicting and maximizing genetic variant discovery via Bayesian nonparametrics
• Collaboration and followership: a stochastic model for activities in social networks
• Homophily and Triadic Closure in Evolving Social Networks
• Urn models with random multiple drawing and random addition