Temporal networks with node-specific memory: unbiased inference of transition probabilities, relaxation times and structural breaks

TL;DR

This paper introduces an unbiased maximum-entropy framework for analyzing temporal networks with node-specific memory, effectively disentangling structural heterogeneity and link persistence to improve inference of network dynamics.

Contribution

It develops an exact analytical solution mapping to a heterogeneous Ising model, enabling better estimation of transition probabilities, relaxation times, and structural breaks in temporal networks.

Findings

Improved estimation of dyadic transition probabilities.

Identification of structural breaks and regime transitions.

Enhanced understanding of node-specific memory effects.

Abstract

One of the main challenges in the study of time-varying networks is the interplay of memory effects with structural heterogeneity. In particular, different nodes and dyads can have very different statistical properties in terms of both link formation and link persistence, leading to a superposition of typical timescales, sub-optimal parametrizations and substantial estimation biases. Here we develop an unbiased maximum-entropy framework to study empirical network trajectories by controlling for the observed structural heterogeneity and local link persistence simultaneously. An exact mapping to a heterogeneous version of the one-dimensional Ising model leads to an analytic solution that rigorously disentangles the hidden variables that jointly determine both static and temporal properties. Additionally, model selection via likelihood maximization identifies the most parsimonious structural level (either global, node-specific or dyadic) accounting for memory effects. As we illustrate on a real-world social network, this method enables an improved estimation of dyadic transition probabilities, relaxation times and structural breaks between dynamical regimes. In the resulting picture, the graph follows a generalized configuration model with given degrees and given time-persisting degrees, undergoing transitions between empirically identifiable stationary regimes.