Learning Methods in Reproducing Kernel Hilbert Space Based on High-dimensional Features Public Deposited

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  • March 20, 2019
Creator
  • Yang, Hojin
    • Affiliation: Gillings School of Global Public Health, Department of Biostatistics
Abstract
  • The first topic focuses on the dimension reduction method via the regularization. We propose the selection for principle components via LASSO. This method assumes that some unknown latent variables are related to the response under the highly correlate covariate structure. L 1 regularization plays a key role in adaptively finding a few liner combinations in contrast to the persistent idea that is to employ a few leading principal components. The consistency of regression coefficients and selected model are asymptotically proved and numerical performances are shown to support our suggestion. The proposed method is applied to analyze microarray data and cancer data. Second and third topics focus on the approaches of the independent screening and the dimension reduction with the machine learning approach using positive definite kernels. A Key ingredient matter of these papers is to use reproducing kernel Hilbert space (RKHS) theory. Specifically, we proposed Multiple Projection Model (MPM) and Single Index Latent Factor Model (SILFM) to build an accurate prediction model for clinical outcomes based on a massive number of features. MPM and SILFM can be summarized as three-stage estimation, screening, dimension reduction, and nonlinear fitting. Screening and dimension reduction are unique approaches of two novel methods. The convergence property of the proposed screening method and the risk bound for SILFM are systematically investigated. The results from several simulation scenarios are shown to support it. The proposed method is applied to analyze brain image data and its clinical behavior response.
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Rights statement
  • In Copyright
Advisor
  • Li, Yun
  • Ibrahim, Joseph
  • Zhu, Hongtu
  • Bair, Eric
  • Gilmore, John
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2016
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