On the Identifiability of the Influence Model for Stochastic Spatiotemporal Spread Processes

TL;DR

This paper investigates the conditions under which the influence model for stochastic spatiotemporal spread processes can be uniquely identified, and develops estimators for model structure, including partially observed cases.

Contribution

It provides necessary and sufficient conditions for influence model identifiability and introduces estimators leveraging the model's unique properties.

Findings

Established conditions for model identifiability

Developed estimators for influence model structure

Analyzed identifiability in partially observed scenarios

Abstract

The influence model is a discrete-time stochastic model that succinctly captures the interactions of a network of Markov chains. The model produces a reduced-order representation of the stochastic network, and can be used to describe and tractably analyze probabilistic spatiotemporal spread dynamics, and hence has found broad usage in network applications such as social networks, traffic management, and failure cascades in power systems. This paper provides sufficient and necessary conditions for the identifiability of the influence model, and also develops estimators for the model structure through exploiting the model's special properties. In addition, we analyze conditions for the identifiability of the partially observed influence model (POIM), for which not all of the sites can be measured.