Statistically Valid Variational Bayes Algorithm for Ising Model Parameter Estimation
针对伊辛模型似然函数归一化常数难计算的问题，用伪似然替代，提出一种计算高效的变分贝叶斯方法，推导了变分后验的收缩率，并通过模拟验证了高斯均值场和二元高斯族的有效性。
Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant in the likelihood. Here, we use a pseudo-likelihood instead, to study the Bayesian estimation of two-parameter, inverse temperature and magnetization, Ising model with a fully specified coupling matrix. We develop a computationally efficient variational Bayes procedure for model estimation. Under the Gaussian mean-field variational family, we derive posterior contraction rates of the variational posterior obtained under the pseudo-likelihood. We also discuss the loss incurred due to variational posterior over true posterior for the pseudo-likelihood approach. Extensive simulation studies validate the efficacy of mean-field Gaussian and bivariate Gaussian families as the possible choices of the variational family for inference of Ising model parameters. Supplementary materials for this article are available online.