Matrix Product Belief Propagation for reweighted stochastic dynamics over graphs

Abstract

Stochastic processes on graphs can describe a great variety of phenomena ranging from neural activity to epidemic spreading. While many existing methods can accurately describe typical realizations of such processes, computing properties of extremely rare events is a hard task. Particularly so in the case of recurrent models, in which variables may return to a previously visited state. Here, we build on the matrix product cavity method, extending it fundamentally in two directions: first, we show how it can be applied to Markov processes biased by arbitrary reweighting factors that concentrate most of the probability mass on rare events. Second, we introduce an efficient scheme to reduce the computational cost of a single node update from exponential to polynomial in the node degree. Two applications are considered: inference of infection probabilities from sparse observations within the SIRS epidemic model, and the computation of both typical observables and large deviations of several kinetic Ising models.

arXiv comment22 pages, 7 figures, 1 table, appendix

References in corpus (19)

• The density-matrix renormalization group in the age of matrix product states
• Matrix product states represent ground states faithfully
• A message passing approach for general epidemic models
• Unsupervised Generative Modeling Using Matrix Product States
• Mean Field Theory For Non-Equilibrium Network Reconstruction
• The Nishimori line and Bayesian Statistics
• Identification of Patient Zero in Static and Temporal Networks - Robustness and Limitations
• A message-passing approach for recurrent-state epidemic models on networks
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Large deviations of cascade processes on graphs
• The Cavity Approach to Parallel Dynamics of Ising Spins on a Graph
• A Cavity Master Equation for the continuous time dynamics of discrete spins models
• A universal form of slow dynamics in zero-temperature random-field Ising model
• Variational approximations for stationary states of Ising-like models
• A simple analytical description of the non-stationary dynamics in Ising spin systems
• A matrix product algorithm for stochastic dynamics on networks, applied to non-equilibrium Glauber dynamics
• Variational approximations for stochastic dynamics on graphs
• The matrix product approximation for the dynamic cavity method
• Perturbative large deviation analysis of non-equilibrium dynamics

Cited by in corpus (6)

• Gauging tensor networks with belief propagation
• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Small-Coupling Dynamic Cavity: a Bayesian mean-field framework for epidemic inference
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
• A short review on the maximum clique problem algorithms with classical, AI, and quantum methods
• Nonequilibrium steady-state dynamics of Markov processes on graphs