Nonlinear modeling based on high-dimensional data

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The development of electronic measurement and instrumentation technologies enables us to accumulate a huge amount of data with complex structure and/or high-dimensional data. Through this research project we have investigated the problem of analyzing such datasets, and proposed various statistical modeling strategies including nonlinear regression modeling via L1 regularization, model evaluation and selection criteria, and Bayesian statistical modeling. Various regularization methods with L1 norm penalty have been investigated both in theoretical and numerical aspects. The problem of evaluating statistical models is a crucial issue in model building process. We proposed various types of model evaluation and selection criteria from both an information-theoretic point of view and a Bayesian approach. The proposed techniques may be used in the extraction of useful information and patterns from data with complex structure in the life sciences, systems engineering, and other fields.