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Accelerating Bayesian estimation for network Poisson models using frequentist variational estimates

Abstract : This work is motivated by the analysis of ecological interaction networks. Poisson stochastic block models are widely used in this field to decipher the structure that underlies a weighted network, while accounting for covariate effects. Efficient algorithms based on variational approximations exist for frequentist inference, but without statistical guaranties as for the resulting estimates. In the absence of variational Bayes estimates, we show that a good proxy of the posterior distribution can be straightforwardly derived from the frequentist variational estimation procedure, using a Laplace approximation. We use this proxy to sample from the true posterior distribution via a sequential Monte Carlo algorithm. As shown in the simulation study, the efficiency of the posterior sampling is greatly improved by the accuracy of the approximate posterior distribution. The proposed procedure can be easily extended to other latent variable models. We use this methodology to assess the influence of available covariates on the organization of several ecological networks, as well as the existence of a residual interaction structure.
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https://hal.inrae.fr/hal-03202058
Contributor : Sophie Donnet Connect in order to contact the contributor
Submitted on : Monday, April 19, 2021 - 2:55:58 PM
Last modification on : Tuesday, September 13, 2022 - 2:14:43 PM

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Sophie Donnet, Stéphane Robin. Accelerating Bayesian estimation for network Poisson models using frequentist variational estimates. Journal of the Royal Statistical Society: Series C Applied Statistics, Wiley, 2021, 70 (4), pp.858-885. ⟨10.1111/rssc.12489⟩. ⟨hal-03202058⟩

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