Nonparametric Bayes Modeling of Populations of Networks

Replicated network data are increasingly available in many research fields. For example, in connectomic applications, interconnections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism...

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Vydané v:Journal of the American Statistical Association Ročník 112; číslo 520; s. 1516 - 1530
Hlavní autori: Durante, Daniele, Dunson, David B., Vogelstein, Joshua T.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Alexandria Taylor & Francis 02.10.2017
Taylor & Francis Group,LLC
Taylor & Francis Ltd
Predmet:
Bayesian analysis
Bayesian nonparametrics
Bayesian theory
Brain
Brain network
Computer simulation
Data
Edge joints
Flexibility
Goodness of fit
Inference
Interconnections
Latent space
Matrix factorization
Morality
Network-valued random variable
Networks
neural networks
Nonparametric statistics
Population distribution
Probabilistic inference
Probabilistic models
Probability
Random variables
Regression analysis
Statistical analysis
Statistical methods
Statistical models
Statistics
Theory and Methods
topology
ISSN:0162-1459, 1537-274X, 1537-274X
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Popis
Shrnutí:Replicated network data are increasingly available in many research fields. For example, in connectomic applications, interconnections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network-valued data. Available models for a single network are not designed specifically for inference on the entire probability mass function of a network-valued random variable and therefore lack flexibility in characterizing the distribution of relevant topological structures. We propose a flexible Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges is defined via a mixture model that reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations. The formulation leads to an efficient Gibbs sampler and provides simple and coherent strategies for inference and goodness-of-fit assessments. We provide theoretical results on the flexibility of our model and illustrate improved performance-compared to state-of-the-art models-in simulations and application to human brain networks. Supplementary materials for this article are available online.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2016.1219260