Network reconstructions with partially available data

Abstract

Many practical systems in natural and social sciences can be described by dynamical networks. Day by day we have measured and accumulated huge amounts of data from these networks, which can be used by us to further our understanding of the world. The structures of the networks producing these data are often unknown. Consequently, understanding the structures of these networks from available data turns to be one of the central issues in interdisciplinary fields, which is called the network reconstruction problem. In this paper, we considered problems of network reconstructions using partially available data and some situations where data availabilities are not sufficient for conventional network reconstructions. Furthermore, we proposed to infer subnetwork with data of the subnetwork available only and other nodes of the entire network hidden; to depict group-group interactions in networks with averages of groups of node variables available; and to perform network reconstructions with known data of node variables only when networks are driven by both unknown internal fast-varying noises and unknown external slowly-varying signals. All these situations are expected to be common in practical systems and the methods and results may be useful for real world applications.

Keywords

network reconstruction / dynamics / data analysis

References

[1] D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature 393(6684), 440 (1998)

[2] A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science 286(5439), 509 (1999)

[3] A. L. Barabási and Z. N. Oltvai, Network biology: Understanding the cell’s functional organization, Nat. Rev. Genet. 5(2), 101 (2004)

[4] A. M. Feist, M. J. Herrgard, I. Thiele, J. L. Reed, and B. O. Palsson, Reconstruction of biochemical networks in microorganisms, Nat. Rev. Microbiol. 7(2), 129 (2008)

[5] R. De Smet and K. Marchal, Advantages and limitations of current network inference methods, Nat. Rev. Microbiol. 8, 717 (2010)

[6] M. K. S. Yeung, J. Tegner, and J. J. Collins, Reverse engineering gene networks using singular value decomposition and robust regression, Proc. Natl. Acad. Sci. USA 99(9), 6163 (2002)

[7] J. M. Stuart, E. Segal, D. Koller, and S. K. Kim, A genecoexpression network for global discovery of conserved genetic modules, Science 302(5643), 249 (2003)

[8] E. Segal, M. Shapira, A. Regev, D. Pe’er, D. Botstein, D. Koller, and N. Friedman, Module networks: Identifying regulatory modules and their condition-specific regulators from gene expression data, Nat. Genet. 34(2), 166 (2003)

[9] Z. Hu, P. J. Killion, and V. R. Iyer, Genetic reconstruction of a functional transcriptional regulatory network, Nat. Genet. 39(5), 683 (2007)

[10] T. R. Lezon, J. R. Banavar, M. Cieplak, A. Maritan, and N. V. Fedoroff, Using the principle of entropy maximization to infer genetic interaction networks from gene expression patterns, Proc. Natl. Acad. Sci. USA 103(50), 19033 (2006)

[11] B. Barzel and A. L. Barabasi, Network link prediction by global silencing of indirect correlations, Nat. Biotechnol. 31(8), 720 (2013)

[12] S. Feizi, D. Marbach, M. Medard, and M. Kellis, Network deconvolution as a general method to distinguish direct dependencies in networks, Nat. Biotechnol. 31(8), 726 (2013)

[13] K. Basso, A. A. Margolin, G. Stolovitzky, U. Klein, R. Dalla-Favera, and A. Califano, Reverse engineering of regulatory networks in human b cells, Nat. Genet. 37(4), 382 (2005)

[14] M. Bansal, V. Belcastro, A. Ambesi-Impiombato, and D. di Bernardo, How to infer gene networks from expression profiles, Mol. Syst. Biol. 3, 78 (2007)

[15] D. Marbach, J. C. Costello, R. Kuffner, N. M. Vega, R. J. Prill, et al, Wisdom of crowds for robust gene network inference, Nat. Methods 9(8), 796 (2012)

[16] A. F. Villaverde, J. Ross, and J. R. Banga, Reverse engineering cellular networks with information theoretic methods, Cells 2(2), 306 (2013)

[17] R. Jansen, H. Yu, D. Greenbaum, Y. Kluger, N. J. Krogan, et al, A bayesian networks approach for predicting protein-protein interactions from genomic data, Science 302(5644), 449 (2003)

[18] N. Friedman, Inferring cellular networks using probabilistic graphical models, Science 303(5659), 799 (2004)

[19] A. C. Haury, F. Mordelet, P. Vera-Licona, and J. P.Vert, Tigress: Trustful inference of gene regulation using stability selection, BMC Syst. Biol. 6(1), 145 (2012)

[20] T. S. Gardner, D. di Bernardo, D. Lorenz, and J. J. Collins, Inferring genetic networks and identifying compound mode of action via expression profiling, Science 301(5629), 102 (2003)

[21] M. W. Covert, E. M. Knight, J. L. Reed, M. J. Herrgard, and B. O. Palsson, Integrating highthroughput and computational data elucidates bacterial networks, Nature 429(6987), 92 (2004)

[22] M. B. Eisen, P. T. Spellman, P. O. Brown, and D. Botstein, Cluster analysis and display of genomewide expression patterns, Proc. Natl. Acad. Sci. USA 95(25), 14863 (1998)

[23] Z. Zhang, Z. Zheng, H. Niu, Y. Mi, S. Wu, and G. Hu, Solving the inverse problem of noise-driven dynamic networks, Phys. Rev. E 91(1), 012814 (2015)

[24] Y. Chen, S. Wang, Z. Zheng, Z. Zhang, and G. Hu, Depicting network structures from variable data produced by unknown colored-noise driven dynamics, Europhys. Lett. 113(1), 18005 (2016)

[25] Y. Chen, Z. Zhang, T. Chen, S. Wang, and G. Hu, Depict noise-driven nonlinear dynamic networks from output data by using high-order correlations, arXiv: 1605.05513

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg