Analysis of Influence Contribution in Social Advertising

Online Social Network (OSN) providers usually conduct advertising campaigns by inserting social ads into promoted posts. Whenever a user engages in a promoted ad, she may further propagate the promoted ad to her followers recursively and the propagation process is known as the word-of-mouth effect. In order to spread the promotion cascade widely and efficiently, the OSN provider often tends to select the influencers, who normally have large audiences over the social network, to initiate the advertising campaign. This marketing model, also termed as influencer marketing, has been gaining increasing traction and investment and is rapidly becoming one of the most widely-used channels in digital marketing. In this paper, we formulate the problem for the OSN provider to derive the influence contributions of influencers given the campaign result, considering the viral propagation of the ads, namely influence contribution allocation (ICA). We make a connection between ICA and the concept of Shapley value in cooperative game theory to reveal the rationale behind ICA. A naive method to obtain the solution to ICA is to enumerate all possible cascades delivering the campaign result, resulting in an exponential number of potential cascades, which is computationally intractable. Moreover, generating a cascade producing the exact campaign result is non-trivial. Facing the challenges, we develop an exact solution in linear time under the linear threshold (LT) model, and devise a fully polynomial-time randomized approximation scheme (FPRAS) under the independent cascade (IC) model. Specifically, under the IC model, we propose an efficient approach to estimate the expected influence contribution in probabilistic graphs modeling OSNs by designing a scalable sampling method with provable accuracy guarantees. We conduct extensive experiments and show that our algorithms yield solutions with remarkably higher quality over several baselines and improve the sampling efficiency significantly.