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Title: Semiparametric regression using variational approximations Authors:  Chong You - University of Nottingham, Ningbo China (China) [presenting]
Francis Hui - Australian National University (Australia)
Samuel Mueller - University of Sydney (Australia)
Han Lin Shang - Australian National University (Australia)
Abstract: Semiparametric regression offers a flexible framework for modeling nonlinear relationships between a response and covariates. A prime example are generalized additive models where for example, spline bases are used with a quadratic penalty to control for overfitting. Estimation and inference is then generally performed either based on penalized likelihood or under a mixed model framework. Penalized likelihood is fast but potentially unstable, and choosing the smoothing parameters needs to be done externally using cross-validation for instance; the mixed model framework tends to be more stable and offers a natural way for choosing the smoothing parameters, but for non-normal responses involves an intractable integral. We present a new framework for semiparametric regression based on variational approximations. The approach possess the stability and natural inference tools of the mixed model framework, while achieving computation times comparable to penalized likelihood. Focusing on GAMs, we derive fully tractable variational likelihoods for some common response types. We present several advantages of the VA framework for inference. We demonstrate consistency of the VA estimates and asymptotic normality for the parametric component.