Browsing by Author "Huo, Shuning"

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    Bayesian Modeling of Complex High-Dimensional Data
    Huo, Shuning (Virginia Tech, 2020-12-07)
    With the rapid development of modern high-throughput technologies, scientists can now collect high-dimensional complex data in different forms, such as medical images, genomics measurements. However, acquisition of more data does not automatically lead to better knowledge discovery. One needs efficient and reliable analytical tools to extract useful information from complex datasets. The main objective of this dissertation is to develop innovative Bayesian methodologies to enable effective and efficient knowledge discovery from complex high-dimensional data. It contains two parts—the development of computationally efficient functional mixed models and the modeling of data heterogeneity via Dirichlet Diffusion Tree. The first part focuses on tackling the computational bottleneck in Bayesian functional mixed models. We propose a computational framework called variational functional mixed model (VFMM). This new method facilitates efficient data compression and high-performance computing in basis space. We also propose a new multiple testing procedure in basis space, which can be used to detect significant local regions. The effectiveness of the proposed model is demonstrated through two datasets, a mass spectrometry dataset in a cancer study and a neuroimaging dataset in an Alzheimer's disease study. The second part is about modeling data heterogeneity by using Dirichlet Diffusion Trees. We propose a Bayesian latent tree model that incorporates covariates of subjects to characterize the heterogeneity and uncover the latent tree structure underlying data. This innovative model may reveal the hierarchical evolution process through branch structures and estimate systematic differences between groups of samples. We demonstrate the effectiveness of the model through the simulation study and a brain tumor real data.
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    Ultra-Fast Approximate Inference Using Variational Functional Mixed Models
    Huo, Shuning; Morris, Jeffrey S.; Zhu, Hongxiao (Taylor & Francis, 2023-04-03)
    While Bayesian functional mixed models have been shown effective to model functional data with various complex structures, their application to extremely high-dimensional data is limited due to computational challenges involved in posterior sampling. We introduce a new computational framework that enables ultra-fast approximate inference for high-dimensional data in functional form. This framework adopts parsimonious basis to represent functional observations, which facilitates efficient compression and parallel computing in basis space. Instead of performing expensive Markov chain Monte Carlo sampling, we approximate the posterior distribution using variational Bayes and adopt a fast iterative algorithm to estimate parameters of the approximate distribution. Our approach facilitates a fast multiple testing procedure in basis space, which can be used to identify significant local regions that reflect differences across groups of samples. We perform two simulation studies to assess the performance of approximate inference, and demonstrate applications of the proposed approach by using a proteomic mass spectrometry dataset and a brain imaging dataset. Supplementary materials for this article are available online.