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Using the price of correlations metric, we show instances where using a seed optimal for Independent Cascade, would hurt the decision maker greatly if an adversarial diffusion process manifests

Correlation Robust Influence Maximization

NIPS 2020, (2020)

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Abstract

We propose a distributionally robust model for the influence maximization problem. Unlike the classic independent cascade model \citep{kempe2003maximizing}, this model's diffusion process is adversarially adapted to the choice of seed set. Hence, instead of optimizing under the assumption that all influence relationships in the network ...More

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Introduction
Highlights
  • Social networks are models that capture transmission of information among its members
  • The Independent Cascade (IC) influence maximization problem - max|S|≤k Eθic [R(c, S)] is known to be NP-hard; even evaluating f ic(S) := Eθic [R(c, S)] for a seed set S is #P-hard (Kempe et al, 2003), though several works have proposed efficient approximation methods, and a greedy algorithm provides a 1 − 1/e − approximation guarantee(Kempe et al, 2003), where > 0 accounts for sampling errors involved in the approximation of f ic(S)
  • We propose to choose a k-sized seed set S that maximizes the expected number of influenced nodes with respect to the worst correlation
  • (2) In Section 4, we show that finding an optimal seed set S that maximizes the worst case expected value R(c, S) is NP-hard
  • While the majority of robust studies for the IC model have considered parameter uncertainty by way of the edge likelihoods, and still assume a fixed correlation structure - namely, independent edge propagation, we study the “reverse’" problem by assuming the edge likelihoods are fixed and the uncertainty lies in how they are correlated
  • Using the price of correlations (POC) metric, we show instances where using a seed optimal for IC, would hurt the decision maker greatly if an adversarial diffusion process manifests
Methods
  • Datasets The authors' experiments were performed on two datasets (1) wikivote: Here each node denotes a user and each edge (i, j) denotes the action of user i voting for user j to be an admin (Leskovec and Krevl, 2014).
  • As in (Yan et al, 2011; Zhang et al, 2014) the authors reverse the edges so that, edge (i, j) in the original graph becomes (j, i)
  • This reverse direction more aptly captures a notion of influence, as user i’s vote for j establishes that user j has influence over user i.
Conclusion
  • The authors have proposed a model for influence maximization where the activation probabilities of the edges are known, but the joint distribution of these activations is unknown, adversarially chosen upon selection of a seed set.
  • For measuring the utility of the model and misspecification under IC, the authors adapt the price of correlations metric for the influence maximization problem.
  • Using the POC metric, the authors show instances where using a seed optimal for IC, would hurt the decision maker greatly if an adversarial diffusion process manifests.
Summary
  • Introduction:

    Social networks are models that capture transmission of information among its members
  • They find applications in testing effectiveness of policies, diffusion of medical innovations, marketing campaigns and news (Yadav et al, 2016; Tambe and Rice, 2018; Hunter and Zaman, 2018; Chen et al, 2011).
  • Objectives:

    The aim of this work is to address the possible pitfalls to the independence assumption in a social network, as used in the study of influence maximization
  • Methods:

    Datasets The authors' experiments were performed on two datasets (1) wikivote: Here each node denotes a user and each edge (i, j) denotes the action of user i voting for user j to be an admin (Leskovec and Krevl, 2014).
  • As in (Yan et al, 2011; Zhang et al, 2014) the authors reverse the edges so that, edge (i, j) in the original graph becomes (j, i)
  • This reverse direction more aptly captures a notion of influence, as user i’s vote for j establishes that user j has influence over user i.
  • Conclusion:

    The authors have proposed a model for influence maximization where the activation probabilities of the edges are known, but the joint distribution of these activations is unknown, adversarially chosen upon selection of a seed set.
  • For measuring the utility of the model and misspecification under IC, the authors adapt the price of correlations metric for the influence maximization problem.
  • Using the POC metric, the authors show instances where using a seed optimal for IC, would hurt the decision maker greatly if an adversarial diffusion process manifests.
Tables
  • Table1: Numerical Summaries of the Graphs from the Datasets
  • Table2: Properties of Sigc and Scgorr for non-identical edge probabilities. k = 40
Download tables as Excel
Related work
  • Related Work and Preliminaries

    There is an extensive literature on influence maximization, including adaptive models (Peng and Chen, 2019), learning (e.g. (Narasimhan et al, 2015; He et al, 2016; Balkanski et al, 2017)), and in recent years, robustness. To the best of our knowledge, robustness in influence maximization first received attention through the parametric perturbation interval model (He and Kempe, 2014) where for each edge (i, j) ∈ E the probability pij is not known exactly, but rather lies in an interval [lij, rij] ⊆ [0, 1]. The model however still assumes all edges are independenty live. Their objective is to obtain the best seed set under the IC model, robust to the values the edge likelihoods p can take. Models of a similar spirit include (Chen et al, 2016; Kalimeris et al, 2018, 2019; Staib et al, 2019). Additionally, (Chen et al, 2016; Kalimeris et al, 2019) study robustness from the view of model misspecification; the particular objectives studied there are hard, partly due to their non-convex and non-submodular objectives. An analogous study of robustness has been performed with the linear threshold model (another diffusion process) in (Nannicini et al, 2019) where the parameters are assumed to be uncertain.
Funding
  • The research of the last three authors was partly supported by the MOE Academic Research Fund Tier 2 grant MOE2019- T2-2-138, “Enhancing Robustness of Networks to Dependence via Optimization”
Study subjects and analysis
cases: 3
Properties of Seed Sets: We now demonstrate some properties of the seed sets Sigc and Scgorr for the case of non-identical probabilities. The following three cases of non-identical probabilities were studied (1) Unif(0, 1): pij drawn i.i.d. from Unif(0, 1); (2) Trivalency: pij drawn i.i.d. from Unif{0.1, 0.01, 0.001}; (3) Weighted cascade: pij = 1/deg(i), deg(i) denotes the number of edges incident to i. In Table 2 we report the mis-specification ratio under alternate diffusion processes -

Reference
  • Abadeh, S. S., Esfahani, P. M. M., and Kuhn, D. (2015). Distributionally robust logistic regression. In Advances in Neural Information Processing Systems, pages 1576–1584.
    Google ScholarLocate open access versionFindings
  • Adamic, L. A. and Glance, N. (2005). The Political Blogosphere and the 2004 U.S. Election: Divided They Blog. In Proceedings of the 3rd International Workshop on Link Discovery, LinkKDD ’05, page 36–43, New York, NY, USA. Association for Computing Machinery.
    Google ScholarLocate open access versionFindings
  • Agrawal, S., Ding, Y., Saberi, A., and Ye, Y. (2012). Price of Correlations in Stochastic Optimization. Operations Research, 60(1):150–162.
    Google ScholarLocate open access versionFindings
  • Aral, S. and Dhillon, P. S. (2018). Social influence maximization under empirical influence models. Nature Human Behaviour, 2(6):375–382.
    Google ScholarLocate open access versionFindings
  • Balkanski, E., Immorlica, N., and Singer, Y. (2017). The importance of communities for learning to influence. In Advances in Neural Information Processing Systems, pages 5862–5871.
    Google ScholarLocate open access versionFindings
  • Chen, L. L., Ma, W., Orlin, J. B., and Simchi-Levi, D. (2020). Distributionally robust max flows. In Symposium on Simplicity in Algorithms, pages 81–90. SIAM.
    Google ScholarLocate open access versionFindings
  • Chen, W., Collins, A., Cummings, R., Ke, T., Liu, Z., Rincón, D., Sun, X., Wang, Y., Wei, W., and Yuan, Y. (2011). Influence maximization in social networks when negative opinions may emerge and propagate. In Microsoft Research Technical Report, pages 379–390.
    Google ScholarLocate open access versionFindings
  • Chen, W., Lakshmanan, L. V., and Castillo, C. (2013). Information and influence propagation in social networks. Synthesis Lectures on Data Management, 5(4):1–177.
    Google ScholarLocate open access versionFindings
  • Chen, W., Lin, T., Tan, Z., Zhao, M., and Zhou, X. (2016). Robust influence maximization. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 795–804.
    Google ScholarLocate open access versionFindings
  • Csardi, G. and Nepusz, T. (2006). The igraph software package for complex network research. InterJournal, Complex Systems:1695.
    Google ScholarLocate open access versionFindings
  • Fathony, R., Rezaei, A., Bashiri, M. A., Zhang, X., and Ziebart, B. (2018). Distributionally robust graphical models. In Advances in Neural Information Processing Systems, pages 8344–8355.
    Google ScholarLocate open access versionFindings
  • He, X. and Kempe, D. (2014). Stability of Influence Maximization. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’14, page 1256–1265, New York, NY, USA. Association for Computing Machinery.
    Google ScholarLocate open access versionFindings
  • He, X., Xu, K., Kempe, D., and Liu, Y. (2016). Learning influence functions from incomplete observations. In Advances in Neural Information Processing Systems, pages 2073–2081.
    Google ScholarLocate open access versionFindings
  • Hunter, D. S. and Zaman, T. (2018). Opinion dynamics with stubborn agents. CoRR, abs/1806.11253.
    Findings
  • Kalimeris, D., Kaplun, G., and Singer, Y. (2019). Robust influence maximization for hyperparametric models. In ICML, volume 97, pages 3192–3200, Long Beach, California, USA. PMLR.
    Google ScholarLocate open access versionFindings
  • Kalimeris, D., Singer, Y., Subbian, K., and Weinsberg, U. (2018). Learning Diffusion using Hyperparameters. In ICML, volume 80, pages 2420–2428.
    Google ScholarLocate open access versionFindings
  • Kempe, D., Kleinberg, J., and Tardos, É. (2003). Maximizing the spread of influence through a social network. In Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, pages 137–146.
    Google ScholarLocate open access versionFindings
  • Klein Haneveld, W. K. (1986). Robustness against dependence in PERT: An application of duality and distributions with known marginals, pages 153–182. Springer Berlin Heidelberg, Berlin, Heidelberg.
    Google ScholarFindings
  • Koçyigit, c., Iyengar, G., Kuhn, D., and Wiesemann, W. (2020). Distributionally robust mechanism design. Management Science, 66(1):159–189.
    Google ScholarLocate open access versionFindings
  • Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J., and Glance, N. (2007). Costeffective outbreak detection in networks. In Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’07, page 420–429, New York, NY, USA. Association for Computing Machinery.
    Google ScholarLocate open access versionFindings
  • Leskovec, J. and Krevl, A. (2014). SNAP Datasets: Stanford large network dataset collection. http://snap.stanford.edu/data.
    Findings
  • Li, Y., Fan, J., Wang, Y., and Tan, K.-L. (2018). Influence maximization on social graphs: A survey. IEEE Transactions on Knowledge and Data Engineering, 30(10):1852–1872.
    Google ScholarLocate open access versionFindings
  • Meilijson, I. and Nádas, A. (1979). Convex majorization with an application to the length of critical paths. Journal of Applied Probability, 16(3):671–677.
    Google ScholarLocate open access versionFindings
  • Minoux, M. (1978). Accelerated greedy algorithms for maximizing submodular set functions. In Stoer, J., editor, Optimization Techniques, pages 234–243, Berlin, Heidelberg. Springer Berlin Heidelberg.
    Google ScholarLocate open access versionFindings
  • Nannicini, G., Sartor, G., Traversi, E., and Wolfler-Calvo, R. (2019). An exact algorithm for robust influence maximization. In Lodi, A. and Nagarajan, V., editors, Integer Programming and Combinatorial Optimization, pages 313–326, Cham. Springer International Publishing.
    Google ScholarLocate open access versionFindings
  • Narasimhan, H., Parkes, D. C., and Singer, Y. (2015). Learnability of influence in networks. In Proceedings of the 28th International Conference on Neural Information Processing Systems Volume 2, NIPS’15, page 3186–3194, Cambridge, MA, USA. MIT Press.
    Google ScholarLocate open access versionFindings
  • Ohsaka, N., Akiba, T., Yoshida, Y., and Kawarabayashi, K.-i. (2014). Fast and accurate influence maximization on large networks with pruned monte-carlo simulations. In AAAI Conference on Artificial Intelligence.
    Google ScholarLocate open access versionFindings
  • Peng, B. and Chen, W. (2019). Adaptive influence maximization with myopic feedback. In Advances in Neural Information Processing Systems 32, pages 5574–5583. Curran Associates, Inc.
    Google ScholarLocate open access versionFindings
  • Staib, M., Wilder, B., and Jegelka, S. (2019). Distributionally robust submodular maximization. In Proceedings of the International Workshop on Artificial Intelligence and Statistics.
    Google ScholarLocate open access versionFindings
  • Tambe, M. and Rice, E. (2018). Artificial Intelligence and Social Work. Cambridge University Press, Cambridge, United Kingdom New York, NY.
    Google ScholarFindings
  • Vaswani, S., Kveton, B., Wen, Z., Ghavamzadeh, M., Lakshmanan, L. V., and Schmidt, M. (2017). Model-independent online learning for influence maximization. In Proceedings of the 34th International Conference on Machine Learning - Volume 70, ICML’17, page 3530–3539. JMLR.org.
    Google ScholarLocate open access versionFindings
  • Watts, D. J. (2002). A simple model of global cascades on random networks. Proceedings of the National Academy of Sciences, 99(9):5766–5771.
    Google ScholarLocate open access versionFindings
  • Wen, Z., Kveton, B., and Ashkan, A. (2015). Efficient Learning in Large-Scale Combinatorial Semi-Bandits. In Bach, F. and Blei, D., editors, Proceedings of the 32nd International Conference on Machine Learning, volume 37 of Proceedings of Machine Learning Research, pages 1113–1122, Lille, France. PMLR.
    Google ScholarLocate open access versionFindings
  • Yadav, A., Chan, H., Xin Jiang, A., Xu, H., Rice, E., and Tambe, M. (2016). Using social networks to aid homeless shelters: Dynamic influence maximization under uncertainty. In Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems, AAMAS ’16, page 740–748, Richland, SC. International Foundation for Autonomous Agents and Multiagent Systems.
    Google ScholarLocate open access versionFindings
  • Yan, Q., Guo, S., and Yang, D. (2011). Influence Maximizing and Local Influenced Community Detection Based on Multiple Spread Model. In Tang, J., King, I., Chen, L., and Wang, J., editors, Advanced Data Mining and Applications, pages 82–95, Berlin, Heidelberg. Springer Berlin Heidelberg.
    Google ScholarLocate open access versionFindings
  • Zhang, P., Chen, W., Sun, X., Wang, Y., and Zhang, J. (2014). Minimizing seed set selection with probabilistic coverage guarantee in a social network. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’14, page 1306–1315, New York, NY, USA. Association for Computing Machinery.
    Google ScholarLocate open access versionFindings
Author
Louis Chen
Louis Chen
Divya Padmanabhan
Divya Padmanabhan
Chee Chin Lim
Chee Chin Lim
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