Belief-Propagation and replicas for inference and learning in a kinetic Ising model with hidden spins

Abstract

We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief Propagation (BP) and Susceptibility Propagation (SusP) can then be used to infer the states of hidden variables and learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the TAP equations for reconstructing the connections.

References in corpus (17)

• The Bethe lattice spin glass revisited
• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Mean Field Theory For Non-Equilibrium Network Reconstruction
• The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods
• Dynamical TAP equations for non-equilibrium Ising spin glasses
• The Cavity Approach to Parallel Dynamics of Ising Spins on a Graph
• Maximum likelihood reconstruction for Ising models with asynchronous updates
• Learning and inference in a nonequilibrium Ising model with hidden nodes
• Market structure explained by pairwise interactions
• Dynamic mean-field and cavity methods for diluted Ising systems
• Inference algorithms for gene networks: a statistical mechanics analysis
• A message-passing scheme for non-equilibrium stationary states
• Network Inference with Hidden Units
• Inferring hidden states in a random kinetic Ising model: replica analysis
• Dynamics and Performance of Susceptibility Propagation on Synthetic Data
• Effect of coupling asymmetry on mean-field solutions of direct and inverse Sherrington-Kirkpatrick model
• Generalized mean field approximation for parallel dynamics of the Ising model

Cited by in corpus (11)

• Inverse statistical problems: from the inverse Ising problem to data science
• Learning with hidden variables
• Inverse Ising problem in continuous time: A latent variable approach
• 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
• 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
• Inference of stochastic time series with missing data
• Critical scaling in hidden state inference for linear Langevin dynamics