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Abstract:
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Neural networks are routinely used for nonparametric regression modeling. The inter-est in these models is growing with ever-increasing complexities in modern datasets. With modern technological advancements, the number of predictors frequently exceeds the sam-ple size in many application areas. Thus selecting important predictors from the huge pool is an extremely important task for judicious inference. However, variable selection within neural net is not well developed. This paper proposes a novel flexible class of Radial Basis Functions (RBF) networks. The proposed architecture can estimate smooth unknown regression functions and also perform variable selection. We primarily focus on Gaussian RBF-net due to its attractive properties. The extensions to other choices of RBF are fairly straightforward. The proposed architecture is also shown to be effective in identifying relevant predictors in a low-dimensional setting without imposing any sparse estimation scheme.We also develop an efficient Markov Chain Monte Carlo algorithm for estimation. We il-lustrate the proposed method’s empirical efficacy through simulation experiments and data application.
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