Inference of kinetic Ising model 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.

9 pages, 3 figures, comments are welcome

References in corpus (9)

• Weak pairwise correlations imply strongly correlated network states in a neural population
• Identification of direct residue contacts in protein-protein interaction by message passing
• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Mean Field Theory For Non-Equilibrium Network Reconstruction
• Parallel dynamics of disordered Ising spin systems on finitely connected random graphs
• The Cavity Approach to Parallel Dynamics of Ising Spins on a Graph
• Dynamical Replica Theory for Disordered Spin Systems
• A message-passing scheme for non-equilibrium stationary states
• Inference and learning in sparse systems with multiple states

Cited by in corpus (15)

• Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems
• Maximum likelihood reconstruction for Ising models with asynchronous updates
• Learning and inference in a nonequilibrium Ising model with hidden nodes
• Universal structural estimator and dynamics approximator for complex networks
• Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
• Inference of the sparse kinetic Ising model using the decimation method
• Inference of the Kinetic Ising Model with Heterogeneous Missing Data
• A matrix product algorithm for stochastic dynamics on networks, applied to non-equilibrium Glauber dynamics
• Dynamical Phase Transitions in Graph Cellular Automata
• Backtracking Dynamical Cavity Method
• The matrix product approximation for the dynamic cavity method
• Dynamics of sparse Boolean networks with multi-node and self-interactions
• Inferring entropy production in many-body systems using nonequilibrium maximum entropy
• Uncovering the non-equilibrium stationary properties in sparse Boolean networks
• Overcoming the complexity barrier of the dynamic message-passing method in networks with fat-tailed degree distributions