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Inferring hidden states in a random kinetic Ising model: replica analysis
Citation key BaRoOp14
Author Ludovica Bachschmid Romano and Manfred Opper
Pages P06013
Year 2014
Journal Journal of Statistical Mechanics: Theory and Experiment
Volume 2014
Number 6
Abstract We consider the problem of predicting the spin states in a kinetic Ising model when spin trajectories are observed for only a finite fraction of sites. In a Bayesian setting, where the probabilistic model of the spin dynamics is assumed to be known, the optimal prediction can be computed from the conditional (posterior) distribution of unobserved spins given the observed ones. Using the replica method, we compute the error of the Bayes optimal predictor for parallel discrete time dynamics in a fully connected spin system with non-symmetric random couplings. The results, exact in the thermodynamic limit, agree very well with simulations of finite spin systems.
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