Estimation of network structures from multivariate point processes

• Material Type: 博士論文
• Title: Estimation of network structures from multivariate point processes
• Author/Editor: 黒田, 佳織
• Author Heading: 黒田, 佳織
• Publication Date: 2014
• Publication Date (W3CDTF): 2014
• Alternative Title: 多変量点過程時系列データを用いたネットワーク構造推定
• Periodical title: 博士論文（埼玉大学大学院理工学研究科（博士後期課程））
• Degree grantor/type: 埼玉大学
• Date Granted: 2014-03-24
• Date Granted (W3CDTF): 2014-03-24
• Dissertation Number: 甲第944号
• Degree Type: 博士(工学)
• Conferring No. (Dissertation): 甲第944号
• Text Language Code: eng
• Target Audience: 一般
• Note (General): type:text; Nonlinear dynamical systems often produce complicated behavior due to interaction between the systems. Such complicated behavior usually depends on connectivity in networks, that is, network topology. Thus, to analyze, model or predict complicated behavior produced from the networks, it is essential to understand the network structures as well as the nonlinear dynamics. Although it is not so easy to investigate the interactions directly, recent developments in measurement technique makes it possible to observe multivariate time series. Then, it is possible to estimate the network structure through the multivariate time series. If an observed time series is continuous and smooth, and sampled by a fixed interval, the network structures can be estimated through statistical measures applied to the continuous time series. However, the nonlinear dynamical systems are often observed as event sequences, for example, firing of neurons, occurrence timing in seismic tremors, transaction timing in stock markets, lightning strike, and so on. Such event sequences are often referred as point processes. It is difficult to directly apply the conventional statistical measures to such point processes. Then, it is an important issue to develop a method to estimate network structures in case that the point processes are observed. In this thesis, we proposed estimation methods of network structures only from the point processes. In the proposed methods, we introduced three strategies: (1) transformation of point processes into continuous time series, (2) using normalized distance between point processes and (3) using multi-dimensional scaling with the distance between point processes. In the first strategy, we applied the method of transforming point processes into continuous time series to detect the connectivity between elements. As the transformation method, we used a kernel density estimator. In the kernel density estimator, we have to select the optimal kernel bandwidth because the transformed time series depends on the bandwidth. Then we proposed two selection methods of the kernel bandwidth: a kernel bandwidth optimization method for estimating firing rates and a selection method of an optimal time delay in the attractor reconstruction which is a basic technique in chaotic time series analysis. By using these bandwidth selection methods in the kernel density estimator, we could reconstruct input information applied neurons from the point processes, and estimate network structures from the point processes. In addition, we treat point processes which have the information of the amplitude and event timing as marked point processes. If we use not only the information of the event timing but also the amplitude information, we can estimate more precisely the network structures. Then we extended the transformation method and the estimation method of network structure to marked point processes. Although these methods work well, one should be careful to apply these methods, because it is possible to lose essential information of point processes by transforming point processes into continuous time series. Then, as the second strategy, we proposed new methods for estimating network structures from point processes by using normalized distance between point processes. Using the distance between point processes, we proposed two measures, a spike time metric coefficient and a partial spike time metric coefficient. The spike time metric coefficient defined by using the normalized distance is a similar measure to the correlation coefficient. Then we applied partialization analysis to the spike time metric coefficient. We experimentally confirmed that these measures can estimate true connectivities from point processes by removing spurious correlations. However, these measures are heuristically defined. Then, to calculate theoretically, we proposed another estimation method by using multi-dimensional scaling with the distance between point processes as the third strategy. We also proposed estimation methods of network structures from marked point processes by using distance between marked point processes. Furthermore, we proposed methods of estimating evolving network structures by dividing the point processes into small temporal epochs and applying the method of estimating static network structures. As a result, the proposed method can estimate the evolving neural network structures and the direction of couplings with high estimation accuracy.; Abstract 11 Introduction 52 Partialization Analysis 92.1 Spurious Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Statistical Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.1 Partial Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Partial Mutual Information . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.3 Partial Directed Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Estimation Method of Network Structure by Transforming Point Processes into Continuous Time Series 233.1 Reconstruction of Input Information from Point Process . . . . . . . . . . . . . . . 243.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.2 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Estimation Method of Network Structure from Simple Point Processes . . . . . . . 343.2.1 Methods of Transforming Point Processes into Continuous Time Series . . 343.2.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3 Estimation Method of Network Structures from Marked Point Processes . . . . . . 433.3.1 Method of Transforming Marked Point Processes into Continuous Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.3.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.4 Summary of Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 Estimation Method of Network Structure Using Distance between Point Processes and Partialization Analysis 494.1 Estimation Method of Network Structure from Simple Point Processes . . . . . . . 504.1.1 Spike Time Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.1.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.2 Estimation Method of Network Structures and direction of couplings from Simple Point Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.2.1 Proposed measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.2.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.3 Summary of Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Estimation Method of Network Structure Using Distance and Multi-Dimensional Scaling 745.1 Estimation Method of Network Structure from Simple Point Process . . . . . . . . 755.1.1 Multi-Dimensional Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . 755.1.2 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Estimation Method of Network Structures from Marked Point Process . . . . . . . 815.2.1 Spike Time Metric for Marked Point Process . . . . . . . . . . . . . . . . 815.2.2 Numerical Simulations and Results . . . . . . . . . . . . . . . . . . . . . 825.3 Estimation of Evolving Network Structure . . . . . . . . . . . . . . . . . . . . . . 885.3.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.3.2 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.4 Summary of Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916 Conclusions 92Publications 98Acknowledgements 101; 主指導教員 : 池口徹教授
• DOI: 10.24561/00010311; https://doi.org/10.24561/00010311
• Persistent ID (NDL): info:ndljp/pid/8977144; https://dl.ndl.go.jp/pid/8977144
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• Collection (particular): 国立国会図書館デジタルコレクション > デジタル化資料 > 博士論文; https://dl.ndl.go.jp/collections/A00014
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• Date Accepted (W3CDTF): 2015-03-01T07:09:42+09:00
• Date Created (W3CDTF): 2015-02-04
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• Periodical Title (URI): http://dx.doi.org/10.24561/00010311; http://id.nii.ac.jp/1586/00010311/
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2023-09-05 再収集