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...Statistical methods with applications to machinelearningandartificial intelligence athesis presented the academic faculty by yibiao lu in partial fulllment of requirements for degree doctor philosophy h milton stewart school industrial and systems engineering georgia institute technology august c copyright approved professor xiaoming huo advisor alex shapiro shi jie deng panagiotis tsiotras daniel guggenheim aerospace ming yuan date apr tableofcontents list tables vi figures vii summary xii i theoreticalresultsonhigh orderlaplacian based regularization function estimation introduction methodology notations problem formulation choice penalty parameter theoretical properties mathematical preparation bounds matrix m s eigenvalues convergence rate multivariate gls estimator asymptotic optimality gcv conclusion appendix detailed proofs agmon theorem neumann boundary condition ii beamlet graph structure path plan ningusingmultiscaleinformation multiscale planning strategy preprocessed inform...