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.

中文翻译：

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使用频率论变分估计加速网络泊松模型的贝叶斯估计

这项工作的动机是对生态相互作用网络的分析。泊松随机块模型广泛用于该领域，以破译作为加权网络基础的结构，同时考虑协变量效应。存在基于变分近似的高效算法用于频率论推理，但对于结果估计没有统计保证。在没有变分贝叶斯估计的情况下，我们表明可以使用拉普拉斯近似从频率论变分估计程序直接导出后验分布的良好代理。我们使用这个代理通过顺序蒙特卡罗算法从真实的后验分布中采样。如模拟研究所示，通过近似后验分布的精度大大提高了后验采样的效率。所提出的程序可以很容易地扩展到其他潜在变量模型。我们使用这种方法来评估可用协变量对几个生态网络组织的影响，以及剩余相互作用结构的存在。