211 research outputs found
Statistical methods for topology inference, denoising, and bootstrapping in networks
Quite 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
Probabilistic methods in the analysis of protein interaction networks
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Change point detection in dynamic Gaussian graphical models: the impact of COVID-19 pandemic on the US stock market
Reliable estimates of volatility and correlation are fundamental in economics
and finance for understanding the impact of macroeconomics events on the market
and guiding future investments and policies. Dependence across financial
returns is likely to be subject to sudden structural changes, especially in
correspondence with major global events, such as the COVID-19 pandemic. In this
work, we are interested in capturing abrupt changes over time in the dependence
across US industry stock portfolios, over a time horizon that covers the
COVID-19 pandemic. The selected stocks give a comprehensive picture of the US
stock market. To this end, we develop a Bayesian multivariate stochastic
volatility model based on a time-varying sequence of graphs capturing the
evolution of the dependence structure. The model builds on the Gaussian
graphical models and the random change points literature. In particular, we
treat the number, the position of change points, and the graphs as object of
posterior inference, allowing for sparsity in graph recovery and change point
detection. The high dimension of the parameter space poses complex
computational challenges. However, the model admits a hidden Markov model
formulation. This leads to the development of an efficient computational
strategy, based on a combination of sequential Monte-Carlo and Markov chain
Monte-Carlo techniques. Model and computational development are widely
applicable, beyond the scope of the application of interest in this work
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