Approximate Variational Estimation for a Model of Network Formation
Approximate Variational Estimation for a Model of Network Formation
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DOI：
10.1162/rest_a_01023
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发表时间：
2017-02
影响因子：
8
通讯作者：
A. Mele;Lingjiong Zhu
中科院分区：
文献类型：
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作者：
A. Mele;Lingjiong Zhu
摘要针对指数随机图模型（ERGMs），提出了一种近似估计方法，其似然性与一个难以处理的归一化常数成正比。通常的方法近似这个常数与蒙特卡洛模拟，但是，收敛可能是指数缓慢。我们提出了一种确定性的方法，基于ERGM的归一化常数的变分平均场近似。我们计算任何网络大小的近似误差的上下界，适应非线性大偏差的结果。这转化为真实似然和平均场似然之间距离的界限。蒙特卡罗模拟表明，在实践中，我们的确定性方法比我们保守的理论近似界限意味着，为一大类模型。
Abstract We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations; however, convergence may be exponentially slow. We propose a deterministic method, based on a variational mean-field approximation of the ERGM's normalizing constant. We compute lower and upper bounds for the approximation error for any network size, adapting nonlinear large deviation results. This translates into bounds on the distance between true likelihood and mean-field likelihood. Monte Carlo simulations suggest that in practice, our deterministic method performs better than our conservative theoretical approximation bounds imply, for a large class of models.