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Open Access Publications from the University of California

Scholarly Works (2 results)

  • Thesis
  • Peer Reviewed
UC Santa Cruz Electronic Theses and Dissertations (2022)

Spectral analysis has been widely used to characterize the properties of one or more time series in the frequency domain. Accurate inference of spectral density matrices is critical for understanding the structure underlying the components of a given multivariate temporal process, and for revealing potential relationships across its components. However, inference of spectral density matrices suffers from the curse of dimensionality. This dissertation first develops methods to estimate the spectral density matrix and functions of this matrix for high-dimensional stationary time series under a Bayesian framework. We consider a Whittle likelihood-based spectral modeling approach and impose a discounted regularized horseshoe prior on the coefficients that define a spline representation of the Cholesky factorization components of the inverse spectral density matrix. Next, we extend the model to estimate the time-varying power spectrum and its functions for high-dimensional nonstationary time series. Under a locally stationary basis representation, two types of priors on basis coefficients are developed: a slow-varying double gamma shrinkage prior is used to induce power spectral estimates to evolve smoothly over time, while a piecewise linear function with a global-local shrinkage prior is proposed for cases in which the power spectral estimates are expected to display abrupt changes. Finally, we further develop methods to conduct quantile spectral analysis for multivariate stationary time series by modeling the matrix of quantile cross-spectral density kernels via its low-rank factorization. Several customized stochastic gradient variational Bayes (SGVB) approaches, supported by parallel computation and GPU accelerations, are developed to obtain fast approximate posterior inference in all the spectral modeling frameworks mentioned above. Extensive simulation studies and data analyses show that our models and methods for posterior inference are accurate and time efficient. Furthermore, our methods are superior compared to competing methods for standard and quantile spectral analysis of multivariate time series.

  • 1 supplemental ZIP
Cover page: Efficient Bayesian Inference on Classical and Quantile Spectral Analysis of Multivariate Time Series
  • Article
  • Peer Reviewed
LBL Publications (2021)
We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented using SAGE graph convolution layers, and trained using an advantage actor critic (A2C) agent. We present two variants, one for finding an edge separator that minimizes the normalized cut or quotient cut, and one that finds a small vertex separator. The vertex separators are then used to construct a nested dissection ordering to permute a sparse matrix so that its triangular factorization will incur less fill-in. The partitioning quality is compared with partitions obtained using METIS and SCOTCH, and the nested dissection ordering is evaluated in the sparse solver SuperLU. Our results show that the proposed method achieves similar partitioning quality as METIS and SCOTCH. Furthermore, the method generalizes across different classes of graphs, and works well on a variety of graphs from the SuiteSparse sparse matrix collection.
    Cover page: Graph Partitioning and Sparse Matrix Ordering using Reinforcement Learning and Graph Neural Networks
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