Inference of kinetic Ising model on sparse graphs

TL;DR

This paper introduces an exact inference method for kinetic Ising models on tree graphs and a good approximation for sparse graphs, outperforming existing mean-field methods by leveraging the dynamical cavity approach.

Contribution

It extends belief propagation to kinetic Ising models, enabling more accurate inference of couplings and fields on sparse networks.

Findings

Outperforms existing mean-field methods on diluted networks.

Provides exact inference on tree graphs.

Offers a good approximation on sparse graphs.

Abstract

Based on dynamical cavity method, we propose an approach to the inference of kinetic Ising model, which asks to reconstruct couplings and external fields from given time-dependent output of original system. Our approach gives an exact result on tree graphs and a good approximation on sparse graphs, it can be seen as an extension of Belief Propagation inference of static Ising model to kinetic Ising model. While existing mean field methods to the kinetic Ising inference e.g., na\" ive mean-field, TAP equation and simply mean-field, use approximations which calculate magnetizations and correlations at time $t$ from statistics of data at time $t-1$, dynamical cavity method can use statistics of data at times earlier than $t-1$ to capture more correlations at different time steps. Extensive numerical experiments show that our inference method is superior to existing mean-field approaches on diluted networks.