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Improving Individual Predictions Using Social Networks Assortativity Improving Individual Predictions using Social Networks Assortativity The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mulders, D. et al. "Improving individual predictions using social networks assortativity" Proceedings of the 12th International Workshop on Self-Organizing Maps and Learning Vector Quantization, Clustering and Data Visualization (WSOM+), June 2017, France, Institute of Electrical and Electronics Engineers (IEEE), 2017 As Published http://wsom2017.loria.fr/ Publisher Institute of Electrical and Electronics Engineers (IEEE) Version Author's final manuscript Citable link http://hdl.handle.net/1721.1/110973 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ Improving Individual Predictions using Social Networks Assortativity Dounia Mulders∗, Cyril de Bodt∗, Johannes Bjellandy, Alex (Sandy) Pentlandz, Michel Verleysen∗ and Yves-Alexandre de Montjoyex;z ∗ ICTEAM institute, Universite´ catholique de Louvain, fdounia.mulders, cyril.debodt, [email protected] y Telenor Research, [email protected] z MIT Media Lab, Massachusetts Institute of Technology, [email protected] x Data Science Institute and Department of Computing, Imperial College London, [email protected] Abstract—Social networks are known to be assortative with such as gender, age, weight, income level, education, race, respect to many attributes, such as age, weight, wealth, level religion, etc. is well documented in the literature [10]–[14]. of education, ethnicity and gender. This can be explained by This property has been theorized to come either from influ- influences and homophilies. Independently of its origin, this ences or homophilies or a combination of both. For instance, assortativity gives us information about each node given its Rosenquiest et al. show that social influence can enhance neighbors. Assortativity can thus be used to improve individual the spreading of alcohol consumption [15] and Madan et al. predictions in a broad range of situations, when data are missing or inaccurate. This paper presents a general framework based on find that weight changes in an individual can be influenced probabilistic graphical models to exploit social network structures by exposure to overweight peers with unhealthy habits or for improving individual predictions of node attributes. Using inactive lifestyles [11]. On the other hand, the concept of this framework, we quantify the assortativity range leading to an homophily is easily understood as the saying goes: “birds of a accuracy gain in several situations. We finally show how specific feather flock together”, which means that people sharing some characteristics of the network can improve performances further. characteristics tend to more communicate. For instance, we For instance, the gender assortativity in real-world mobile phone observe more connections between people of the same age data changes significantly according to some communication and gender [10]. attributes. In this case, individual predictions with 75% accuracy Independently of its cause, this assortativity can be used for are improved by up to 3%. individual prediction purposes when some labels are missing Keywords—Belief propagation, assortativity, homophily, social or uncertain, e.g. for demographics prediction in large net- networks, mobile phone metadata. works. Some methods are currently developed to exploit that assortativity [2], [16]. However, few studies take the global I. INTRODUCTION network structure into account [5], [17]. Also, to the best of Social networks currently drive an increasing attention our knowledge, no research quantifies how the performances in the research community, as they are found in diverse are related to the assortativity strength. situations and are described by huge amounts of data notably We here propose a framework based on probabilistic graph- collected through the web and mobile devices. Facebook, ical models (PGMs) to exploit the social network structure Twitter, Google+, mobile phone networks and other large- for individual prediction improvement in a general context. scale social graphs are nowadays largely studied for predicting The method can be applied while only knowing the labels and analyzing individual demographics [1]–[3]. This type of a limited number of pairs of connected users in order to of information is indeed a key input for the establishment evaluate the assortativity, and class probability estimates for of economic and social policies, health campaigns, market each user. These probabilities may for example be obtained segmentation, etc. [3]–[5]. Nevertheless, especially (but not by applying a machine learning algorithm exploiting the node- exclusively) in developing countries, such statistics are often level information, after it has been trained on the individual scarce or even lacking, as local censuses are costly, rough, data of the users with known labels. A loopy belief propagation time-consuming and hence rarely up-to-date [6]. This is the algorithm is applied on a Markov random field modeling the reason why recent researches address this problem by inferring network to improve the accuracy of these prior class probabil- demographics from large social networks [4], [7], in order to ity estimates. The model is able to benefit from the strength ease the access of policy makers and NGO’s toward more of the links, quantified for example by the number of contacts. reliable information. The estimation of the network assortativity allows to optimally Social networks contain individual information about their tune the model parameters, by defining synthetic graphs. The users (e.g. generated tweets for Twitter), in addition to a latter simulations permit (1) to prevent overfitting a given (real) graph topology information. These graphs present specific network structure, (2) to perform the parameter tuning off-line structures carrying many different characteristics, such as and (3) to avoid requiring the labeled users to form a connected small-worldness or heterogeneous degree distribution [8]. The graph. These simulations also allow to quantify the assor- assortativity of social networks, defined as the nodes tendency tativity range leading to an accuracy gain over an approach to be linked to others which are similar in some sense [9], ignoring the network structure. The methodology is validated with respect to various demographics of their individuals on mobile phone data to predict gender. As the assortativity 978-1-5090-6638-4/17/$31.00 c 2017 IEEE required to significantly improve the quality of the prior class Please cite as: Mulders, D., de Bodt, C., Bjelland, J., Pentland, A., Verleysen, M., & de Montjoye, Y.-A. (2017). Improving individual predictions using social networks assortativity. Proceedings of the 12th International Workshop on Self-Organizing Maps and Learning Vector Quantization, Clustering and Data Visualization (WSOM+), pp. 127-134. probabilities might not always be reached in practice, we show that the assortativity significantly changes according to some communication attributes, which can in turn be exploited to improve the predictions by appropriately adapting the model parameters in different parts of the network. The paper is organized as follows. The general methodol- ogy to improve attribute predictions in a network is detailed in Section II. Its key parameters are highlighted and their tuning based on simulated assortative networks is detailed. In Section III, we introduce the real-world data sets which are studied, analyze their underlying gender homophilies and Fig. 1. Toy example of the MRF. There are two nodes per user i in the assess the performances of our method compared to a baseline graph, Yi being her class and Xi her individual data. algorithm. Section IV then discusses the results, while summa- rizing the related work. Conclusions are drawn in Section V. In the following, uppercase and lowercase letters denote indicated by the graph separation property [20], the joint respectively random variables and observed values. probability distribution p(Y;X) modeled by the PGM, where Y (resp. X) concatenates all the Y ’s (resp. X ’s), admits II. METHOD i i the factorization p (y; x) = p (y) · Q p (x jy ). The Given an arbitrary social network G, the goal is to exploit Y ;X Y XijYi i i i its assortativity to infer, for each user i, an individual scalar underlying assumption is that Xi given Yi is independent from attribute (or class) Yi taking values in a finite alphabet Y. This Yj and Xj, for all j 6= i. class can be, for instance, the age or gender of each individual. We choose a nonmaximal cliques representation through G is defined as a pair (V; E), where V and E are respectively pairwise interactions for the distribution pY (y), allowing to the sets of nodes (one for each user) and edges (connecting considerably reduce the inference cost at the expense of taking each pair of individuals who are in contact), with jVj = N. into account higher order relationships, leading to The available individual information about user i is denoted by 1 Y Y the vector Xi. In the case of Twitter, xi consists in the tweets p (y; x) = (y ; x ) Ψ(y ; y ); (1) Y ;X Z i i j k generated by user i, and possibly in public profile details (e.g. i (j;k)2E the user’s name). It is assumed that estimates pY jX (y jxi) of b i i i where Z is a normalization constant and and Ψ are the class membership probabilities pYijXi (yijxi) are provided. These can be seen as “initial predictions” for each user i 2 V, called the node and edge potentials respectively. By identi- fication with the previous factorization, the ith node potential which can encode deterministic information (known labels) p (y jx ) YijXi i i or which can be outputted by a machine learning algorithm (yi; xi) = pXijYi (xijyi) / corresponds to the pYi (yi) applied on the individual features xi to predict the class yi. likelihood of the ith user’s individual data knowing her class. If such information is missing for some users, uniform class It can be estimated using the first predicted class probability probabilities are used.
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