### Abstract

Complex networks hosting binary-state dynamics arise in a variety of contexts. In spite of previous works, to fully reconstruct the network structure from observed binary data remains challenging. We articulate a statistical inference based approach to this problem. In particular, exploiting the expectation-maximization (EM) algorithm, we develop a method to ascertain the neighbors of any node in the network based solely on binary data, thereby recovering the full topology of the network. A key ingredient of our method is the maximum-likelihood estimation of the probabilities associated with actual or nonexistent links, and we show that the EM algorithm can distinguish the two kinds of probability values without any ambiguity, insofar as the length of the available binary time series is reasonably long. Our method does not require any a priori knowledge of the detailed dynamical processes, is parameter-free, and is capable of accurate reconstruction even in the presence of noise. We demonstrate the method using combinations of distinct types of binary dynamical processes and network topologies, and provide a physical understanding of the underlying reconstruction mechanism. Our statistical inference based reconstruction method contributes an additional piece to the rapidly expanding "toolbox" of data based reverse engineering of complex networked systems.

Original language | English (US) |
---|---|

Article number | 022301 |

Journal | Physical Review E |

Volume | 97 |

Issue number | 2 |

DOIs | |

State | Published - Feb 5 2018 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E*,

*97*(2), [022301]. https://doi.org/10.1103/PhysRevE.97.022301

**Statistical inference approach to structural reconstruction of complex networks from binary time series.** / Ma, Chuang; Chen, Han Shuang; Lai, Ying-Cheng; Zhang, Hai Feng.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 97, no. 2, 022301. https://doi.org/10.1103/PhysRevE.97.022301

}

TY - JOUR

T1 - Statistical inference approach to structural reconstruction of complex networks from binary time series

AU - Ma, Chuang

AU - Chen, Han Shuang

AU - Lai, Ying-Cheng

AU - Zhang, Hai Feng

PY - 2018/2/5

Y1 - 2018/2/5

N2 - Complex networks hosting binary-state dynamics arise in a variety of contexts. In spite of previous works, to fully reconstruct the network structure from observed binary data remains challenging. We articulate a statistical inference based approach to this problem. In particular, exploiting the expectation-maximization (EM) algorithm, we develop a method to ascertain the neighbors of any node in the network based solely on binary data, thereby recovering the full topology of the network. A key ingredient of our method is the maximum-likelihood estimation of the probabilities associated with actual or nonexistent links, and we show that the EM algorithm can distinguish the two kinds of probability values without any ambiguity, insofar as the length of the available binary time series is reasonably long. Our method does not require any a priori knowledge of the detailed dynamical processes, is parameter-free, and is capable of accurate reconstruction even in the presence of noise. We demonstrate the method using combinations of distinct types of binary dynamical processes and network topologies, and provide a physical understanding of the underlying reconstruction mechanism. Our statistical inference based reconstruction method contributes an additional piece to the rapidly expanding "toolbox" of data based reverse engineering of complex networked systems.

AB - Complex networks hosting binary-state dynamics arise in a variety of contexts. In spite of previous works, to fully reconstruct the network structure from observed binary data remains challenging. We articulate a statistical inference based approach to this problem. In particular, exploiting the expectation-maximization (EM) algorithm, we develop a method to ascertain the neighbors of any node in the network based solely on binary data, thereby recovering the full topology of the network. A key ingredient of our method is the maximum-likelihood estimation of the probabilities associated with actual or nonexistent links, and we show that the EM algorithm can distinguish the two kinds of probability values without any ambiguity, insofar as the length of the available binary time series is reasonably long. Our method does not require any a priori knowledge of the detailed dynamical processes, is parameter-free, and is capable of accurate reconstruction even in the presence of noise. We demonstrate the method using combinations of distinct types of binary dynamical processes and network topologies, and provide a physical understanding of the underlying reconstruction mechanism. Our statistical inference based reconstruction method contributes an additional piece to the rapidly expanding "toolbox" of data based reverse engineering of complex networked systems.

UR - http://www.scopus.com/inward/record.url?scp=85042112203&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevE.97.022301

DO - 10.1103/PhysRevE.97.022301

M3 - Article

VL - 97

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 2

M1 - 022301

ER -