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

TL;DR

This paper introduces a novel inference algorithm combining Belief Propagation and replicas for hidden spins in a kinetic Ising model, improving connection reconstruction and hidden state inference from observed data.

Contribution

It presents a new algorithm leveraging replicated auxiliary spins to simplify likelihood calculation and enhance inference in kinetic Ising models with hidden spins.

Findings

Outperforms TAP equations in connection reconstruction

Effective for networks with Gaussian and binary bonds

Converges well with varying hidden node fractions

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.