Tree-reweighted近似によるIsing逆問題の解

Abstract

To develop an efficient and accurate method for learning in the Ising model, we apply the tree-reweighted approximation to compute the partition function. Using the tree-reweighted approximation, we can optimize the rigorous lower bound of the exact objective function. By solving the moment-matching and self-consistency conditions analytically, we can derive the interaction matrix as a function of the given data statistics. With this solution, we can obtain the optimal interaction matrix without iterative computation. To evaluate the accuracy of the proposed inverse formula, we compared our results to those obtained by existing inverse formulae obtained by other approximations. In an experiment to reconstruct the interaction matrix, we found that the proposed formula returns the best estimates in strongly-attractive regions for various graph structures.