Learning Influence Functions from Incomplete Observations

TL;DR

This paper addresses learning influence functions in social networks with incomplete data, proposing methods with theoretical guarantees and practical algorithms that perform well even with significant missing observations.

Contribution

It introduces both proper and improper PAC learning methods for influence functions under incomplete observations, including reductions and parametrizations with theoretical and empirical validation.

Findings

Proper PAC learnability via graph modifications

Improper PAC learning with reachability features

Effective handling of large missing data fractions in experiments

Abstract

We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missing observations. Proper PAC learnability under the Discrete-Time Linear Threshold (DLT) and Discrete-Time Independent Cascade (DIC) models is established by reducing incomplete observations to complete observations in a modified graph. Our improper PAC learnability result applies for the DLT and DIC models as well as the Continuous-Time Independent Cascade (CIC) model. It is based on a parametrization in terms of reachability features, and also gives rise to an efficient and practical heuristic. Experiments on synthetic and real-world datasets demonstrate the ability of our method to compensate even for a fairly large fraction of missing observations.