- Physical Review Journals
All JournalsPhysics Magazine

Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Node Metadata Can Produce Predictability Crossovers in Network Inference Problems

Oscar Fajardo-Fontiveros1,‡, Roger Guimerà2,1,*, and Marta Sales-Pardo1,†

  • 1Department of Chemical Engineering, Universitat Rovira i Virgili, 43007 Tarragona, Catalonia
  • 2ICREA, 08010 Barcelona, Catalonia

  • *Corresponding author. roger.guimera@urv.cat
  • †Corresponding author. marta.sales@urv.cat
  • ‡oscar.fajardo@urv.cat
PDF

Phys. Rev. X 12, 011010 – Published 14 January, 2022

DOI: https://doi.org/10.1103/PhysRevX.12.011010

Abstract

Network inference is the process of learning the properties of complex networks from data. Besides using information about known links in the network, node attributes and other forms of network metadata can help solve network inference problems. Indeed, several approaches have been proposed to introduce metadata into probabilistic network models and to use them to make better inferences. However, we know little about the effect of such metadata in the inference process. Here, we investigate this issue. We find that, rather than affecting inference gradually, adding metadata causes a crossover in the inference process and in our ability to make accurate predictions, from a situation in which metadata do not play any role to a situation in which metadata completely dominate the inference process. When network data and metadata are partly correlated, metadata optimally contributes to the inference process at the crossover between data-dominated and metadata-dominated regimes.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Predicting whether two drugs have a harmful interaction or whether someone is going to like a certain movie are examples of network inference problems. In these problems, the goal is to predict new interactions (between drugs or between people and movies) based on some previously observed interactions. Having additional information about the network nodes or their metadata (for example, the mechanism of action of the drugs or the age of the individuals) helps to make better predictions, though it is not clear why or how. Here, we explore how that improvement happens.

We study a very general network inference problem and show that node metadata do not affect the inference problem gradually. Rather, even when the importance assigned to the metadata increases smoothly, the inference process crosses over from a data-dominated regime to a metadata-dominated regime. These crossovers show some similarities to transitions driven by temperature, where one finds energy- and entropy-dominated regimes. Importantly, optimal inference is often encountered exactly at this crossover.

Our study opens the door to better understanding the role of metadata in network inference problems and, more broadly, establishes further connections between general inference problems and physical concepts such as phase transitions.

Article Text

References (40)

  1. D. Liben-Nowell and J. Kleinberg, The Link-Prediction Problem for Social Networks, J. Am. Soc. Inf. Sci. Technol. 58, 1019 (2007).
  2. A. Clauset, C. Moore, and M. E. J. Newman, Hierarchical Structure and the Prediction of Missing Links in Networks., Nature (London) 453, 98 (2008).
  3. R. Guimerà and M. Sales-Pardo, Missing and Spurious Interactions and the Reconstruction of Complex Networks., Proc. Natl. Acad. Sci. U.S.A. 106, 22073 (2009).
  4. L. Lü, L. Pan, T. Zhou, Y.-C. Zhang, and H. E. Stanley, Toward Link Predictability of Complex Networks, Proc. Natl. Acad. Sci. U.S.A. 112, 2325 (2015).
  5. A. Ghasemian, H. Hosseinmardi, A. Galstyan, E. M. Airoldi, and A. Clauset, Stacking Models for Nearly Optimal Link Prediction in Complex Networks, Proc. Natl. Acad. Sci. U.S.A. 117, 23393 (2020).
  6. R Guimerà, One Model to Rule Them All in Network Science?, Proc. Natl. Acad. Sci. U.S.A. 117, 25195 (2020).
  7. R. Guimerà and M. Sales-Pardo, A Network Inference Method for Large-Scale Unsupervised Identification of Novel Drug-Drug Interactions, PLoS Comput. Biol. 9, e1003374 (2013).
  8. M. Tarrés-Deulofeu, A. Godoy-Lorite, R. Guimerà, and M. Sales-Pardo, Tensorial and Bipartite Block Models for Link Prediction in Layered Networks and Temporal Networks, Phys. Rev. E 99, 032307 (2019).
  9. M. P. Menden et al., Community Assessment to Advance Computational Prediction of Cancer Drug Combinations in a Pharmacogenomic Screen, Nat. Commun. 10, 2674 (2019).
  10. R. Guimerà and M. Sales-Pardo, Justice Blocks and Predictability of U.S. Supreme Court Votes, PLoS One 6, e27188 (2011).
  11. R. Guimerà, A. Llorente, E. Moro, and M. Sales-Pardo, Predicting Human Preferences Using the Block Structure of Complex Social Networks, PLoS One 7, e44620 (2012).
  12. A. Godoy-Lorite, R. Guimerà, C. Moore, and M. Sales-Pardo, Accurate and Scalable Social Recommendation Using Mixed-Membership Stochastic Block Models, Proc. Natl. Acad. Sci. U.S.A. 113, 14207 (2016).
  13. S. Cobo-López, A. Godoy-Lorite, J. Duch, M. Sales-Pardo, and R. Guimerà, Optimal Prediction of Decisions and Model Selection in Social Dilemmas Using Block Models, Eur. Phys. J. Data Sci. 7, 48 (2018).
  14. G. Poux-Médard, S. Cobo-López, J. Duch, R. Guimerà, and M. Sales-Pardo, Complex Decision-Making Strategies in a Stock Market Experiment Explained as the Combination of Few Simple Strategies, Eur. Phys. J. Data Sci 10, 26 (2021).
  15. M. Timme, Revealing Network Connectivity from Response Dynamics, Phys. Rev. Lett. 98, 224101 (2007).
  16. T. P. Peixoto, Network Reconstruction and Community Detection from Dynamics, Phys. Rev. Lett. 123, 128301 (2019).
  17. C. Tallberg, A Bayesian Approach to Modeling Stochastic Blockstructures with Covariates, J. Math. Sociol. 29, 1 (2004).
  18. J. Yang, J. McAuley, and J. Leskovec, Community Detection in Networks with Node Attributes, in 2013 IEEE 13th International Conference on Data Mining (2013), pp. 1151–1156, 10.1109/ICDM.2013.167.
  19. Y. Zhu, X. Yan, L. Getoor, and C. Moore, Scalable Text and Link Analysis with Mixed-Topic Link Models, in Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’13 (Association for Computing Machinery, New York, 2013), p. 473–481, 10.1145/2487575.2487693.
  20. D. Hric, T. P. Peixoto, and S. Fortunato, Network Structure, Metadata, and the Prediction of Missing Nodes and Annotations, Phys. Rev. X 6, 031038 (2016).
  21. M. E. J. Newman and A. Clauset, Structure and Inference in Annotated Networks, Nat. Commun. 7, 11863 (2016).
  22. A. White and T. B. Murphy, Mixed-Membership of Experts Stochastic Blockmodel, Netw. Sci. 4, 48 (2016).
  23. L. Peel, D. B. Larremore, and A. Clauset, The Ground Truth About Metadata and Community Detection in Networks, Sci. Adv. 3, e1602548 (2017), 10.1126/sciadv.1602548.
  24. N. Stanley, T. Bonacci, and R. Kwitt, Stochastic Block Models with Multiple Continuous Attributes, Appl. Netw. Sci. 4, 54 (2019).
  25. M. Contisciani, E. A. Power, and C. De Bacco, Community Detection with Node Attributes in Multilayer Networks, Sci. Rep. 10, 15736 (2020).
  26. Y. Koren, R. Bell, and C. Volinsky, Matrix Factorization Techniques for Recommender Systems, Computer 42, 30 (2009).
  27. A. Decelle, F. Krzakala, C. Moore, and L. Zdeborová, Inference and Phase Transitions in the Detection of Modules in Sparse Networks, Phys. Rev. Lett. 107, 065701 (2011).
  28. F. Radicchi, Detectability of Communities in Heterogeneous Networks, Phys. Rev. E 88, 010801(R) (2013).
  29. F. Radicchi, A Paradox in Community Detection, Europhys. Lett. 106, 38001 (2014).
  30. P. Zhang, C. Moore, and L. Zdeborová, Phase Transitions in Semisupervised Clustering of Sparse Networks, Phys. Rev. E 90, 052802 (2014).
  31. P. W. Holland, K. B. Laskey, and S. Leinhardt, Stochastic Blockmodels: First Steps, Soc. Networks 5, 109 (1983).
  32. K. Nowicki and T. A. B. Snijders, Estimation and Prediction for Stochastic Blockstructures, J. Am. Stat. Assoc. 96, 1077 (2001).
  33. T.-C. Yen and D. B. Larremore, Community Detection in Bipartite Networks with Stochastic Block Models, Phys. Rev. E 102, 032309 (2020).
  34. E. M. Airoldi, D. M. Blei, S. E Fienberg, and E. P. Xing, Mixed Membership Stochastic Blockmodels, J. Mach. Learn. Res. 9, 1981 (2008).
  35. E. T. Jaynes, Information Theory and Statistical Mechanics, Phys. Rev. 106, 620 (1957).
  36. E. T. Jaynes, Information Theory and Statistical Mechanics. II, Phys. Rev. 108, 171 (1957).
  37. F. M. Harper and J. A. Konstan, The Movielens Datasets: History and Context, ACM Trans. Interact. Intell. Syst. 5, 19 (2015).
  38. A. S. Waugh, L. Pei, J. Fowler, P. Mucha, and M. A. Porter, Party Polarization in Congress: A Network Science Approach, arXiv:0907.3509v3.

  39. The task of predicting ratings considered here is a generalization of the task of link prediction that allows for (i) unobserved links (that is, links whose existence is unknown) and (ii) more than two states for each link (that is, it goes beyond exists or does not exist). Indeed, the standard link-prediction problem can be mapped exactly to our rating-prediction problem by assign “rating 1” to all links and “rating 0” to all nonlinks in a network; with this mapping, all the discussion in the paper remains valid, and we are strictly solving the link prediction problem in a regular network.

  40. Strictly speaking, EM gives a local maximum of the posterior rather than the global MAP.

Outline

Information

Phys. Rev. X 12, 011010– Published 14 January, 2022
  • Received 8 April 2021
  • Accepted 16 November 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation