Inferring hidden states in a random kinetic Ising model: replica analysis

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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• Network Inference with Hidden Units
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• Data-driven inference of hidden nodes in networks
• Inferring hidden states in Langevin dynamics on large networks: Average case performance
• Inference for dynamics of continuous variables: the Extended Plefka Expansion with hidden nodes
• Learning of couplings for random asymmetric kinetic Ising models revisited: random correlation matrices and learning curves
• The appropriateness of ignorance in the inverse kinetic Ising model
• Characterizing spreading dynamics of subsampled systems with non-stationary external input
• Inference of stochastic time series with missing data
• Critical scaling in hidden state inference for linear Langevin dynamics