{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:19:16Z","timestamp":1760231956736,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T00:00:00Z","timestamp":1651449600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarships Council","doi-asserted-by":"publisher","award":["201906310134","EP\/N510129\/1","IES\\R2\\192206"],"award-info":[{"award-number":["201906310134","EP\/N510129\/1","IES\\R2\\192206"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012338","name":"Alan Turing Institute","doi-asserted-by":"publisher","award":["201906310134","EP\/N510129\/1","IES\\R2\\192206"],"award-info":[{"award-number":["201906310134","EP\/N510129\/1","IES\\R2\\192206"]}],"id":[{"id":"10.13039\/100012338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"publisher","award":["201906310134","EP\/N510129\/1","IES\\R2\\192206"],"award-info":[{"award-number":["201906310134","EP\/N510129\/1","IES\\R2\\192206"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Using observational data to infer the coupling structure or parameters in dynamical systems is important in many real-world applications. In this paper, we propose a framework of strategically influencing a dynamical process that generates observations with the aim of making hidden parameters more easily inferable. More specifically, we consider a model of networked agents who exchange opinions subject to voting dynamics. Agent dynamics are subject to peer influence and to the influence of two controllers. One of these controllers is treated as passive and we presume its influence is unknown. We then consider a scenario in which the other active controller attempts to infer the passive controller\u2019s influence from observations. Moreover, we explore how the active controller can strategically deploy its own influence to manipulate the dynamics with the aim of accelerating the convergence of its estimates of the opponent. Along with benchmark cases we propose two heuristic algorithms for designing optimal influence allocations. We establish that the proposed algorithms accelerate the inference process by strategically interacting with the network dynamics. Investigating configurations in which optimal control is deployed. We first find that agents with higher degrees and larger opponent allocations are harder to predict. Second, even factoring in strategical allocations, opponent\u2019s influence is typically the harder to predict the more degree-heterogeneous the social network.<\/jats:p>","DOI":"10.3390\/e24050640","type":"journal-article","created":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T08:26:35Z","timestamp":1651566395000},"page":"640","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Control Meets Inference: Using Network Control to Uncover the Behaviour of Opponents"],"prefix":"10.3390","volume":"24","author":[{"given":"Zhongqi","family":"Cai","sequence":"first","affiliation":[{"name":"School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enrico","family":"Gerding","sequence":"additional","affiliation":[{"name":"School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Markus","family":"Brede","sequence":"additional","affiliation":[{"name":"School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"343001","DOI":"10.1088\/1751-8113\/47\/34\/343001","article-title":"Revealing networks from dynamics: An introduction","volume":"47","author":"Timme","year":"2014","journal-title":"J. Phys. Math. Theor."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1109\/TSIPN.2020.2990276","article-title":"Bayesian inference of network structure from information cascades","volume":"6","author":"Gray","year":"2020","journal-title":"IEEE Trans. Signal Inf. Process. Over Networks"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3154524","article-title":"Network structure inference, a survey: Motivations, methods, and applications","volume":"51","author":"Brugere","year":"2018","journal-title":"ACM Comput. Surv. (CSUR)"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1093\/bioinformatics\/btv672","article-title":"Optimal design of gene knockout experiments for gene regulatory network inference","volume":"32","author":"Gunawan","year":"2016","journal-title":"Bioinformatics"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Huynh-Thu, V.A., and Sanguinetti, G. (2019). Gene regulatory network inference: An introductory survey. Gene Regulatory Networks, Springer.","DOI":"10.1007\/978-1-4939-8882-2"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"David, O., Guillemain, I., Saillet, S., Reyt, S., Deransart, C., Segebarth, C., and Depaulis, A. (2008). Identifying neural drivers with functional MRI: An electrophysiological validation. PLoS Biol., 6.","DOI":"10.1371\/journal.pbio.0060315"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Papalexakis, E.E., Fyshe, A., Sidiropoulos, N.D., Talukdar, P.P., Mitchell, T.M., and Faloutsos, C. (2014, January 24\u201327). Good-enough brain model: Challenges, algorithms and discoveries in multi-subject experiments. Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA.","DOI":"10.1145\/2623330.2623639"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"20180844","DOI":"10.1098\/rsif.2018.0844","article-title":"Network reconstruction from infection cascades","volume":"16","author":"Braunstein","year":"2019","journal-title":"J. R. Soc. Interface"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s11222-019-09865-1","article-title":"Epidemiologic network inference","volume":"30","author":"Barbillon","year":"2020","journal-title":"Stat. Comput."},{"key":"ref_10","unstructured":"Myers, S., and Leskovec, J. (2010, January 6\u201311). On the convexity of latent social network inference. Proceedings of the Twenty-Fourth Conference on Neural Information Processing Systems, Vancouver, BC, Canada."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1608","DOI":"10.1109\/TCSI.2018.2886770","article-title":"Reconstructing of networks with binary-state dynamics via generalized statistical inference","volume":"66","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Circuits Syst. Regul. Pap."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Guo, C., and Luk, W. (2013, January 2\u20134). Accelerating maximum likelihood estimation for hawkes point processes. Proceedings of the 2013 23rd International Conference on Field programmable Logic and Applications, Porto, Portugal.","DOI":"10.1109\/FPL.2013.6645502"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1852","DOI":"10.1109\/TKDE.2018.2807843","article-title":"Influence maximization on social graphs: A survey","volume":"30","author":"Li","year":"2018","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.geb.2014.09.002","article-title":"Competitive contagion in networks","volume":"113","author":"Goyal","year":"2019","journal-title":"Games Econ. Behav."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"e0252515","DOI":"10.1371\/journal.pone.0252515","article-title":"Shadowing and shielding: Effective heuristics for continuous influence maximisation in the voting dynamics","volume":"16","author":"Chakraborty","year":"2021","journal-title":"PLoS ONE"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1093\/comnet\/cny027","article-title":"Effects of time horizons on influence maximization in the voter dynamics","volume":"7","author":"Brede","year":"2019","journal-title":"J. Complex Networks"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Cai, Z., Brede, M., and Gerding, E. (2020, January 1\u20133). Influence maximization for dynamic allocation in voter dynamics. Proceedings of the International Conference on Complex Networks and Their Applications, Madrid, Spain.","DOI":"10.1007\/978-3-030-65347-7_32"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Nguyen, N.P., Yan, G., Thai, M.T., and Eidenbenz, S. (2012, January 22\u201324). Containment of misinformation spread in online social networks. Proceedings of the 4th Annual ACM Web Science Conference, Evanston, IL, USA.","DOI":"10.1145\/2380718.2380746"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Galam, S., and Javarone, M.A. (2016). Modeling radicalization phenomena in heterogeneous populations. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0155407"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Hegselmann, R., K\u00f6nig, S., Kurz, S., Niemann, C., and Rambau, J. (2014). Optimal opinion control: The campaign problem. arXiv.","DOI":"10.2139\/ssrn.2516866"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"033031","DOI":"10.1088\/1367-2630\/17\/3\/033031","article-title":"Opinion control in complex networks","volume":"17","author":"Masuda","year":"2015","journal-title":"New J. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.crhy.2019.05.004","article-title":"Reality-inspired voter models: A mini-review","volume":"20","author":"Redner","year":"2019","journal-title":"Comptes Rendus Phys."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Romero Moreno, G., Manino, E., Tran-Thanh, L., and Brede, M. (2020). Zealotry and influence maximization in the voter model: When to target partial zealots?. Complex Networks XI, Springer.","DOI":"10.1007\/978-3-030-40943-2_10"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"032303","DOI":"10.1103\/PhysRevE.95.032303","article-title":"Universal data-based method for reconstructing complex networks with binary-state dynamics","volume":"95","author":"Li","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"032317","DOI":"10.1103\/PhysRevE.97.032317","article-title":"Sparse dynamical Boltzmann machine for reconstructing complex networks with binary dynamics","volume":"97","author":"Chen","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_26","unstructured":"Cai, Z., Gerding, E., and Brede, M. (December, January 30). Accelerating Opponent Strategy Inference for Voting Dynamics on Complex Networks. Proceedings of the International Conference on Complex Networks and Their Applications, Madrid, Spain."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Masucci, A.M., and Silva, A. (2014, January 1\u20133). Strategic resource allocation for competitive influence in social networks. Proceedings of the 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA.","DOI":"10.1109\/ALLERTON.2014.7028557"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2086737.2086741","article-title":"Inferring networks of diffusion and influence","volume":"5","author":"Leskovec","year":"2012","journal-title":"ACM Trans. Knowl. Discov. Data (TKDD)"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-031-01850-3","article-title":"Information and influence propagation in social networks","volume":"5","author":"Chen","year":"2013","journal-title":"Synth. Lect. Data Manag."},{"key":"ref_30","unstructured":"Rodriguez, M.G., and Sch\u00f6lkopf, B. (2012). Submodular inference of diffusion networks from multiple trees. arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"He, X., and Liu, Y. (2017, January 6\u201310). Not Enough Data? Joint Inferring Multiple Diffusion Networks via Network Generation Priors. Proceedings of the Tenth ACM International Conference on Web Search and Data Mining, Cambridge, UK.","DOI":"10.1145\/3018661.3018675"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s41060-018-0156-4","article-title":"Motif-aware diffusion network inference","volume":"9","author":"Tan","year":"2020","journal-title":"Int. J. Data Sci. Anal."},{"key":"ref_33","unstructured":"Ramezani, M., Rabiee, H.R., Tahani, M., and Rajabi, A. (2017). Dani: A fast diffusion aware network inference algorithm. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1111\/1467-9469.00296","article-title":"Bayesian inference for stochastic epidemics in populations with random social structure","volume":"29","author":"Britton","year":"2002","journal-title":"Scand. J. Stat."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.jtbi.2004.07.026","article-title":"Network theory and SARS: Predicting outbreak diversity","volume":"232","author":"Meyers","year":"2005","journal-title":"J. Theor. Biol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1103\/RevModPhys.81.591","article-title":"Statistical physics of social dynamics","volume":"81","author":"Castellano","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Leskovec, J., Backstrom, L., and Kleinberg, J. (2009\u20131, January 28). Meme-tracking and the dynamics of the news cycle. Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Paris, France.","DOI":"10.1145\/1557019.1557077"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Br\u00e9maud, P. (2020). Non-homogeneous Markov Chains. Markov Chains, Springer.","DOI":"10.1007\/978-3-030-45982-6_12"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/S0022-2496(02)00028-7","article-title":"Tutorial on maximum likelihood estimation","volume":"47","author":"Myung","year":"2003","journal-title":"J. Math. Psychol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.jmp.2017.05.006","article-title":"A tutorial on Fisher information","volume":"80","author":"Ly","year":"2017","journal-title":"J. Math. Psychol."},{"key":"ref_41","unstructured":"Press, W., Teukolsky, S., Vetterling, W., and Flannery, B. (2007). Section 10.11. Linear programming: Interior-point methods. Numerical Recipes: The Art of Scientific Computing, Cambridge University Press."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevE.71.027103","article-title":"Generation of Uncorrelated Random Scale-Free Networks","volume":"71","author":"Catanzaro","year":"2005","journal-title":"Phys. Rev. E"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/640\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:05:30Z","timestamp":1760137530000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/640"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,2]]},"references-count":42,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["e24050640"],"URL":"https:\/\/doi.org\/10.3390\/e24050640","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,5,2]]}}}