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 (6)

• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Mean Field Theory For Non-Equilibrium Network Reconstruction
• Dynamical TAP equations for non-equilibrium Ising spin glasses
• Inference algorithms for gene networks: a statistical mechanics analysis
• Inferring hidden states in a random kinetic Ising model: replica analysis
• Dynamics and Performance of Susceptibility Propagation on Synthetic Data

Cited by in corpus (3)

• 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