Nonbacktracking Bounds on the Influence in Independent Cascade Models

TL;DR

This paper introduces new upper and lower bounds on influence spread in independent cascade models using nonbacktracking walks, enhancing accuracy and computational efficiency through message passing and trade-off controls.

Contribution

It applies nonbacktracking walks and FKG inequalities to influence estimation, providing a novel approach with adjustable accuracy and efficiency.

Findings

Bounds are tighter than existing methods.

Trade-off parameter effectively balances accuracy and computation.

Simulations demonstrate the bounds' tightness across network models.

Abstract

This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin-Kasteleyn-Ginibre (FKG) type inequalities, and are computed by message passing implementation. Nonbacktracking walks have recently allowed for headways in community detection, and this paper shows that their use can also impact the influence computation. Further, we provide a knob to control the trade-off between the efficiency and the accuracy of the bounds. Finally, the tightness of the bounds is illustrated with simulations on various network models.