Naslov
Differentiating between Exogenous and Endogenous Information Propagation in Social Networks

Autori
Piškorec, Matija ; Šmuc, Tomislav ; Šikić, Mile

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Second International Workshop on Data Science : Abstract Book / - , 2017, 39-41

Skup
Second International Workshop on Data Science

Mjesto i datum
Zagreb, Hrvatska, 30.11.2017

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
peer and external influence ; social network

Sažetak
Rising popularity of social networks allows us to investigate dynamics of social interactions on a scale that would be unimaginable just a couple of decades ago. One particular kind of social interaction is information propagation between users of online social network, which we can divide into that which is endogenous - propagating between users (peers), and that which is exogenous - originating from external information sources like online mass media. In fact, large information cascades in social networks are often driven by exogenous events such as political unrest and natural disasters. In this work we propose a model of social influence which is conceptually similar to the unified model of social influence [2] which was shown to be generalization of many popular influence models, including complex contagion model, independent cascade model and generalized threshold model. At each time step all activated users attempt to activate all of their peers in network with certain probability. Also, there is an external influence which acts equally on all users at a given time step, although it may change over time. Activation times of each individual user are known, and together they form an activation cascade. Our problem is then the following: Given particular form of peer influence along with activation cascade and a network of users, infer parameters of peer and external influence while assuming that parameters of peer influence stay constant throughout the 39 Machine Learning and Data Mining Thursday, 10:40-11:05 period while external influence may change in time. Similar attempts exist in lit- erature, including peer and authority model [1] which, however, requires explicit modeling of authorities responsible for external influence. Also, we try to decou- ple the endogenous and exogenous influence just by using a statistical properties of activation cascades on network without inferring the actual exposure curves. We assume that information propagation in online social networks is mediated by two influences: (i) peer influence which is endogenous to the network, and (ii) external influence which is exogenous to the network. As these two influences are often confounded we are interested in inferring them separately from our observed data - friendship network of users and their activation times, given some functional forms for peer and external influence. We will do this by optimizing a log-likelihood function which gives us a probabilistic description of our problem. The log-likelihood is evaluated in moving time windows and it separates users into those that did or did not activate at a particular time window. The formulation is flexible enuogh to allow for parameters of peer and external influence to vary for each user and each time window. However, we choose to constrain the inference problem in order to better estimate the maximum likelihood solution. First, we choose functional forms for peer and external influence. For simplicity, we will model external influence as a constant probability of activation which acts on all yet nonactivated users at a specific time. For the peer influence models we will choose several models typically encountered in literature: (i) Susceptible- infected model, (ii) Exponential decay model, and (iii) Logistic threshold model. To constrain optimization problem even more we introduce some simplifying assumptions: (i) all users have equal parameters of peer influence, (ii) external influence acts equally to all users at a specific time window, and (iii) parameters of peer influence do not change over time. Because our model gives us probabilities for peer activation as well as for external activation for each user, we can use this information to estimate activation type for each of the users. We can also define a single measure of external responsibility which quantifies to what extent is an activation of each user due to the external influence. To empirically validate our methodology we use two Facebook applications as online political polls one week prior to the upcoming referendum (referen- dum2013.hr dataset, over ten thousand users) and parliamentary elections (sa- bor2015.hr dataset, over six thousand users) in Croatia. To our knowledge these are the largest Facebook datasets obtained in this way as users had to give an explicit consent to participate in the study. We consider an act of registration as an activation event, and infer the magnitude of endogenous and exogenous influence for each Facebook user in the activation cascade. We estimate magni- tude of endogenous and exogenous influence by performing maximum likelihood estimation using various peer influence models. Length of the time window used 40 Thursday, 10:40-11:05 Machine Learning and Data Mining for evaluating log-likelihood is 30 minutes. We compare our method with a base- line method that classifies an activation as external if the user had no previously activated friends. This is a conservative measure that tends to underestimate the true external influence because after majority of users is activated it is extremely unlikely for newly activated users to have no previously activated friends, even if they really are activated by an external influence. We estimate a separate exoge- nous influence parameter at each time window and a single set of parameters for endogenous influence. The results for the exponential decay model indicate that the half-decay of peer influence is approximately 5 hours. This is expected, as it is reasonable to assume that engagement of users in sharing specific information is halved in a timespan of several hours, and probably decays to zero after a day or two. We also expect for endogenous influence to be smooth and slowly varying, while exogenous influence has sharp spikes of activity which are aligned with the times when major online news providers reported on our application.

Izvorni jezik
Engleski

Znanstvena područja
Računarstvo

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