Learning and inference in a nonequilibrium Ising model with hidden nodes

Abstract

We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.

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• Mean Field Theory For Non-Equilibrium Network Reconstruction
• Mean-field theory for the inverse Ising problem at low temperatures
• Dynamical TAP equations for non-equilibrium Ising spin glasses
• Market structure explained by pairwise interactions
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• Bayesian Mechanics for Stationary Processes
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• Inference of the Kinetic Ising Model with Heterogeneous Missing Data
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• Sparse model selection in the highly under-sampled regime
• 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
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• Critical scaling in hidden state inference for linear Langevin dynamics