Sample complexity bounds for influence maximization

Gal Sadeh, Edith Cohen, Haim Kaplan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Influence maximization (IM) is the problem of finding for a given s ≥ 1 a set S of |S| = s nodes in a network with maximum influence. With stochastic diffusion models, the influence of a set S of seed nodes is defined as the expectation of its reachability over simulations, where each simulation specifies a deterministic reachability function. Two well-studied special cases are the Independent Cascade (IC) and the Linear Threshold (LT) models of Kempe, Kleinberg, and Tardos [31]. The influence function in stochastic diffusion is unbiasedly estimated by averaging reachability values over i.i.d. simulations. We study the IM sample complexity: the number of simulations needed to determine a (1 − )-approximate maximizer with confidence 1 − δ. Our main result is a surprising upper bound of O(sτ−2 ln nδ ) for a broad class of models that includes IC and LT models and their mixtures, where n is the number of nodes and τ is the number of diffusion steps. Generally τ n, so this significantly improves over the generic upper bound of O(sn−2 ln nδ ). Our sample complexity bounds are derived from novel upper bounds on the variance of the reachability that allow for small relative error for influential sets and additive error when influence is small. Moreover, we provide a data-adaptive method that can detect and utilize fewer simulations on models where it suffices. Finally, we provide an efficient greedy design that computes an (1 − 1/e − )-approximate maximizer from simulations and applies to any submodular stochastic diffusion model that satisfies the variance bounds.

Original languageEnglish
Title of host publication11th Innovations in Theoretical Computer Science Conference, ITCS 2020
EditorsThomas Vidick
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771344
DOIs
StatePublished - Jan 2020
Event11th Innovations in Theoretical Computer Science Conference, ITCS 2020 - Seattle, United States
Duration: 12 Jan 202014 Jan 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume151
ISSN (Print)1868-8969

Conference

Conference11th Innovations in Theoretical Computer Science Conference, ITCS 2020
Country/TerritoryUnited States
CitySeattle
Period12/01/2014/01/20

Keywords

  • Influence maximization
  • Sample complexity
  • Submodular maximization

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