Optimization of Continuous Parameters by a Binary Hopfield Network with Application to an Estimation Problem

Abstract

Binary Hopfield networks are shown to be effective in estimation of Gaussian random vectors based on partial observation. Estimation with maximum likelihood is replaced by minimization of a quadratic cost. The energy-decreasing property of Hopfield networks is applied to the minimization by making the network energy equivalent to the quadratic cost. It is proved that existence of the local minima of the network energy leads to no practical problem provided the network contains sufficiently abundant units. The resultant network is composed of subnetworks with mutually equal number of units. The activity ratio of each subnetwork represents a component of a given random vector. If some of the subnetworks are cramped in accordance with observed data, the rest of the subnetworks reconstruct the most probable values of the unobserved components of the random vector. A simulation result suggests that the network behavior is insensitive to partial damage in the connections between the units of the network.