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dc.contributor.advisorKolaczyk, Eric D.en_US
dc.contributor.authorKang, Xinyuen_US
dc.date.accessioned2019-01-18T14:43:48Z
dc.date.available2019-01-18T14:43:48Z
dc.date.issued2018
dc.identifier.urihttps://hdl.handle.net/2144/33117
dc.description.abstractQuite often, the data we observe can be effectively represented using graphs. The underlying structure of the resulting graph, however, might contain noise and does not always hold constant across scales. With the right tools, we could possibly address these two problems. This thesis focuses on developing the right tools and provides insights in looking at them. Specifically, I study several problems that incorporate network data within the multi-scale framework, aiming at identifying common patterns and differences, of signals over networks across different scales. Additional topics in network denoising and network bootstrapping will also be discussed. The first problem we consider is the connectivity changes in dynamic networks constructed from multiple time series data. Multivariate time series data is often non-stationary. Furthermore, it is not uncommon to expect changes in a system across multiple time scales. Motivated by these observations, we in-corporate the traditional Granger-causal type of modeling within the multi-scale framework and propose a new method to detect the connectivity changes and recover the dynamic network structure. The second problem we consider is how to denoise and approximate signals over a network adjacency matrix. We propose an adaptive unbalanced Haar wavelet based transformation of the network data, and show that it is efficient in approximation and denoising of the graph signals over a network adjacency matrix. We focus on the exact decompositions of the network, the corresponding approximation theory, and denoising signals over graphs, particularly from the perspective of compression of the networks. We also provide a real data application on denoising EEG signals over a DTI network. The third problem we consider is in network denoising and network inference. Network representation is popular in characterizing complex systems. However, errors observed in the original measurements will propagate to network statistics and hence induce uncertainties to the summaries of the networks. We propose a spectral-denoising based resampling method to produce confidence intervals that propagate the inferential errors for a number of Lipschitz continuous net- work statistics. We illustrate the effectiveness of the method through a series of simulation studies.en_US
dc.language.isoen_US
dc.subjectStatisticsen_US
dc.subjectNetworken_US
dc.subjectGraphical modelen_US
dc.subjectMultiscale modelingen_US
dc.titleStatistical methods for topology inference, denoising, and bootstrapping in networksen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2018-11-13T17:02:06Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplineMathematics & Statisticsen_US
etd.degree.grantorBoston Universityen_US


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