{"title": "Multistage Campaigning in Social Networks", "book": "Advances in Neural Information Processing Systems", "page_first": 4718, "page_last": 4726, "abstract": "We consider control problems for multi-stage campaigning over social networks. The dynamic programming framework is employed to balance the high present reward and large penalty on low future outcome in the presence of extensive uncertainties. In particular, we establish theoretical foundations of optimal campaigning over social networks where the user activities are modeled as a multivariate Hawkes process, and we derive a time dependent linear relation between the intensity of exogenous events and several commonly used objective functions of campaigning. We further develop a convex dynamic programming framework for determining the optimal intervention policy that prescribes the required level of external drive at each stage for the desired campaigning result. Experiments on both synthetic data and the real-world MemeTracker dataset show that our algorithm can steer the user activities for optimal campaigning much more accurately than baselines.", "full_text": "Multistage Campaigning in Social Networks\n\nMehrdad Farajtabar\u2217\n\nXiaojing Ye\u22c4\n\nSahar Harati\u2020\n\nGeorgia Institute of Technology\u2217\n\nLe Song\u2217\n\nHongyuan Zha\u2217\n\nGeorgia State University\u22c4\n\nEmory University\u2020\n\nmehrdad@gatech.edu\n\nxye@gsu.edu\n\nsahar.harati@emory.edu\n\n{lsong,zha}@cc.gatech.edu\n\nAbstract\n\nWe consider the problem of how to optimize multi-stage campaigning over social\nnetworks. The dynamic programming framework is employed to balance the high\npresent reward and large penalty on low future outcome in the presence of exten-\nsive uncertainties. In particular, we establish theoretical foundations of optimal\ncampaigning over social networks where the user activities are modeled as a mul-\ntivariate Hawkes process, and we derive a time dependent linear relation between\nthe intensity of exogenous events and several commonly used objective functions\nof campaigning. We further develop a convex dynamic programming framework\nfor determining the optimal intervention policy that prescribes the required level\nof external drive at each stage for the desired campaigning result. Experiments on\nboth synthetic data and the real-world MemeTracker dataset show that our algo-\nrithm can steer the user activities for optimal campaigning much more accurately\nthan baselines.\n\n1 Introduction\nObama was the \ufb01rst US president in history who successfully leveraged online social media in pres-\nidential campaigning, which has been popularized and become a ubiquitous approach to electoral\npolitics (such as in the on-going 2016 US presidential election) in contrast to the decreasing rele-\nvance of traditional media such as TV and newspapers [1, 2]. The power of campaigning via social\nmedia in modern politics is a consequence of online social networking being an important part of\npeople\u2019s regular daily social lives. It has been quite common that individuals use social network sites\nto share their ideas and comment on other people\u2019s opinions. In recent years, large organizations,\nsuch as governments, public media, and business corporations, also start to announce news, spread\nideas, and/or post advertisements in order to steer the public opinion through social media platform.\nThere has been extensive interest for these entities to in\ufb02uence the public\u2019s view and manipulate\nthe trend by incentivizing in\ufb02uential users to endorse their ideas/merits/opinions at certain monetary\nexpenses or credits. To obtain most cost-effective trend manipulations, one needs to design an opti-\nmal campaigning strategy or policy such that quantities of interests, such as in\ufb02uence of opinions,\nexposure of a campaign, adoption of new products, can be maximized or steered towards the target\namount given realistic budget constraints.\nThe key factor differentiating social networks from traditional media is peer in\ufb02uence. In fact, events\nin an online social network can be categorized roughly into two types: endogenous events where\nusers just respond to the actions of their neighbors within the network, and exogenous events where\nusers take actions due to drives external to the network. Then it is natural to raise the following\nfundamental questions regarding optimal campaigning over social networks: can we model and\nexploit those event data to steer the online community to a desired exposure level? More speci\ufb01cally,\ncan we drive the overall exposure to a campaign to a certain level (e.g., at least twice per week per\nuser) by incentivizing a small number of users to take more initiatives? What about maximizing the\noverall exposure for a target group of people?\n\n30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain.\n\n\fMore importantly, those exposure shaping tasks are more effective when the interventions are imple-\nmented in multiple stages. Due to the inherent uncertainty in social behavior, the outcome of each\nintervention may not be fully predictable but can be anticipated to some extent before the next in-\ntervention happens. A key aspect of such situations is that interventions can\u2019t be viewed in isolation\nsince one must balance the desire for high present reward with the penalty of low future outcome.\nIn this paper, the dynamic programming framework [3] is employed to tackle the aforementioned\nissues. In particular, we \ufb01rst establish the fundamental theory of optimal campaigning over social\nnetworks where the user activities are modeled as a multivariate Hawkes process (MHP) [4, 5] since\nMHP can capture both endogenous and exogenous event intensities. We also derive a time dependent\nlinear relation between the intensity of exogenous events and the overall exposure to the campaign.\nExploiting this connection, we develop a convex dynamic programming framework for determining\nthe optimal intervention policy that prescribes the required level of external drive at each stage in\norder for the campaign to reach a desired exposure pro\ufb01le. We propose several objective functions\nthat are commonly considered as campaigning criteria in social networks. Experiments on both\nsynthetic data and real world network of news websites in the MemeTracker dataset show that our\nalgorithms can shape the exposure of campaigns much more accurately than baselines.\n2 Basics and Background\nAn n-dimensional temporal point process is a random process whose realization consists of a\nlist of discrete events in time and their associated dimension, {(tk, dk)} with tk \u2208 R+ and\ndk \u2208{ 1, . . . , n}. Many different types of data produced in online social networks can be rep-\nresented as temporal point processes, such as likes and tweets. A temporal point process can be\nequivalently represented as a counting process, N (t) = (N 1(t), . . . ,N n(t))\u22a4 associated to n users\nin the social network. Here, N i(t) records the number of events user i performs before time t for\n1 \u2264 i \u2264 n. Let the history Hi(t) be the list of times of events {t1, t2, . . . , tk} of the i-th user up\nto time t. Then, the number of observed events in a small time window [t, t + dt) of length dt is\ndN i(t) =!tk\u2208Hi(t) \u03b4(t \u2212 tk) dt, and hence N i(t) =\" t\n0 dN i(s), where \u03b4(t) is a Dirac delta func-\ntion. The point process representation of temporal data is fundamentally different from the discrete\ntime representation typically used in social network analysis. It directly models the time interval\nbetween events as random variables, avoids the need to pick a time window to aggregate events, and\nallows temporal events to be modeled in a \ufb01ne grained fashion. Moreover, it has a remarkably rich\ntheoretical support [6].\nAn important way to characterize temporal point processes is via the conditional intensity function\n\u2014 a stochastic model for the time of the next event given all the times of previous events. Formally,\nthe conditional intensity function \u03bbi(t) (intensity, for short) of user i is the conditional probability\n\nof observing an event in a small window [t, t + dt) given the history H(t) =#H1(t), . . . ,Hn(t)$:\n\n\u03bbi(t)dt := P{user i performs event in [t, t + dt)|H(t)} = E[dN i(t)|H(t)],\n\n(1)\nwhere one typically assumes that only one event can happen in a small window of size dt. The\nfunctional form of the intensity \u03bbi(t) is often designed to capture the phenomena of interests.\nThe Hawkes process [7] is a class of self and mutually exciting point process models,\n\n\u03bbi(t) = \u00b5i(t) + %k:tk