Approximate Variational Estimation for a Model of Network Formation
针对指数随机图模型似然函数中难以计算的归一化常数，提出一种基于平均场变分近似的确定性估计方法，并给出任意网络规模下的误差上下界，蒙特卡洛模拟表明该方法在实际中优于理论保守界。
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.