All Times ET
Keywords: Ising model, Variational Bayes, Pseudo-likelihood, Stochastic Optimization
We have studied two dimensional Ising model parameter estimation with a fully specified coupling matrix of size n by n, given only one observed data vector from the Ising model. In our Bayesian approach, the parameters (beta, B) of the Ising model are viewed as random variables with prior distributions. We have used the variational Bayes (VB) method in order to estimate the parameters. For implementing the variational inference (VI) procedure, we postulate a couple of variational families and find the optimal variational distribution which is close to the true posterior distribution in terms of Kullback-Leibler (KL) divergence. Also, we employ pseudo-likelihood of the Ising model to avoid dealing with an intractable normalizing constant. In order to implement the VB with pseudo-likelihood, stochastic optimization is used. The simulation result shows that the VI estimates are close to the true parameters and robust along with the different value of the degree for the coupling matrix.