Information Source Finding in Networks: Querying With Budgets

In this paper, we study a problem of detecting the source of diffused information by querying individuals, given a sample snapshot of the information diffusion graph, where two queries are asked: <italic>(i)</italic> whether the respondent is the source or not, and <italic>(ii)</italic> if not, which neighbor spreads the information to the respondent. We consider the case when respondents may not always be truthful and some cost is taken for each query. Our goal is to quantify the necessary and sufficient budgets to achieve the detection probability <inline-formula> <tex-math notation="LaTeX">$1-\delta $ </tex-math></inline-formula> for any given <inline-formula> <tex-math notation="LaTeX">$0< \delta < 1$ </tex-math></inline-formula>. To this end, we study two types of algorithms: adaptive and non-adaptive ones, each of which corresponds to whether we adaptively select the next respondents based on the answers of the previous respondents or not. We first provide the information theoretic lower bounds for the necessary budgets in both algorithm types. In terms of the sufficient budgets, we propose two practical estimation algorithms, each of non-adaptive and adaptive types, and for each algorithm, we quantitatively analyze the budget which ensures <inline-formula> <tex-math notation="LaTeX">$1-\delta $ </tex-math></inline-formula> detection accuracy. This theoretical analysis not only quantifies the budgets needed by practical estimation algorithms achieving a given target detection accuracy in finding the diffusion source, but also enables us to quantitatively characterize the amount of extra budget required in non-adaptive type of estimation, referred to as <italic>adaptivity gap</italic>. We validate our theoretical findings over synthetic and real-world social network topologies.

[1]  Jaeyoung Choi,et al.  Estimating the rumor source with anti-rumor in social networks , 2016, 2016 IEEE 24th International Conference on Network Protocols (ICNP).

[2]  Wanlei Zhou,et al.  K-Center: An Approach on the Multi-Source Identification of Information Diffusion , 2015, IEEE Transactions on Information Forensics and Security.

[3]  Luc Devroye,et al.  Finding Adam in random growing trees , 2014, Random Struct. Algorithms.

[4]  Jure Leskovec,et al.  Predicting positive and negative links in online social networks , 2010, WWW '10.

[5]  Feng Ji,et al.  An Algorithmic Framework for Estimating Rumor Sources With Different Start Times , 2017, IEEE Transactions on Signal Processing.

[6]  Lei Ying,et al.  Information source detection in networks: Possibility and impossibility results , 2016, IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications.

[7]  Devavrat Shah,et al.  Rumors in a Network: Who's the Culprit? , 2009, IEEE Transactions on Information Theory.

[8]  Devavrat Shah,et al.  Rumor centrality: a universal source detector , 2012, SIGMETRICS '12.

[9]  Wanlei Zhou,et al.  Identifying Propagation Source in Time-Varying Networks , 2018, Malicious Attack Propagation and Source Identification.

[10]  Lei Ying,et al.  Catch'Em All: Locating Multiple Diffusion Sources in Networks with Partial Observations , 2016, AAAI.

[11]  Christos Faloutsos,et al.  Efficiently spotting the starting points of an epidemic in a large graph , 2013, Knowledge and Information Systems.

[12]  Jure Leskovec,et al.  Learning to Discover Social Circles in Ego Networks , 2012, NIPS.

[13]  Devavrat Shah,et al.  Detecting sources of computer viruses in networks: theory and experiment , 2010, SIGMETRICS '10.

[14]  Enhong Chen,et al.  Information Source Detection via Maximum A Posteriori Estimation , 2015, 2015 IEEE International Conference on Data Mining.

[15]  Wuqiong Luo,et al.  Finding an infection source under the SIS model , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[16]  Jaeyoung Choi,et al.  Rumor source detection under querying with untruthful answers , 2017, IEEE INFOCOM 2017 - IEEE Conference on Computer Communications.

[17]  Wuqiong Luo,et al.  How to Identify an Infection Source With Limited Observations , 2013, IEEE Journal of Selected Topics in Signal Processing.

[18]  Ashish Khetan,et al.  Achieving budget-optimality with adaptive schemes in crowdsourcing , 2016, NIPS.

[19]  Alexandre Proutière,et al.  Community Detection via Random and Adaptive Sampling , 2014, COLT.

[20]  Chee Wei Tan,et al.  Rooting out the rumor culprit from suspects , 2013, 2013 IEEE International Symposium on Information Theory.

[21]  Chee Wei Tan,et al.  Rumor source detection with multiple observations: fundamental limits and algorithms , 2014, SIGMETRICS '14.

[22]  Po-Ling Loh,et al.  Confidence Sets for the Source of a Diffusion in Regular Trees , 2015, IEEE Transactions on Network Science and Engineering.

[23]  Vivek S. Borkar,et al.  Temporally Agnostic Rumor-Source Detection , 2017, IEEE Transactions on Signal and Information Processing over Networks.

[24]  Hongyuan Zha,et al.  Back to the Past: Source Identification in Diffusion Networks from Partially Observed Cascades , 2015, AISTATS.

[25]  Lei Ying,et al.  Information source detection in the SIR model: A sample path based approach , 2012, 2013 Information Theory and Applications Workshop (ITA).

[26]  Yaron Singer,et al.  Influence maximization through adaptive seeding , 2016, SECO.

[27]  Jaeyoung Choi,et al.  Necessary and Sufficient Budgets in Information Source Finding with Querying: Adaptivity Gap , 2018, 2018 IEEE International Symposium on Information Theory (ISIT).

[28]  Sujay Sanghavi,et al.  Learning the graph of epidemic cascades , 2012, SIGMETRICS '12.

[29]  Kaito Fujii,et al.  Beyond Adaptive Submodularity: Approximation Guarantees of Greedy Policy with Adaptive Submodularity Ratio , 2019, ICML.