Bayesian Nonparametrics via Neural Networks
Bayesian Nonparametrics via Neural Networks is the first book to focus on neural networks in the context of nonparametric regression and classification, working within the Bayesian paradigm. It discusses neural networks in a statistical context, an approach in contrast to existing books, which tend to treat neural networks as a machine learning algorithm instead of a statistical model. Once this underlying statistical model is recognized, other standard statistical techniques can be applied to improve the model. The Bayesian approach allows better accounting for uncertainty. This book covers uncertainty in model choice and ways to deal with this issue, exploring ideas from statistics and machine learning. An analysis on the choice of prior and new noninformative priors is included, along with a substantial literature review. Written for statisticians using statistical terminology, this book will lead statisticians to an increased understanding of the neural network model and its applicability to real-world problems.
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American Statistical Association applications approximation bagging basis representation basis set Bayes factors Bayesian bootstrap Berger Breiman choice of prior classification coefficients compute correlated covariates current model dataset Denote density discussion equation estimate example explanatory variables Figure fitted function fitted values flat prior Friedman Gaussian hidden nodes hyperparameters improper indicator function input Jeffreys prior layer linear combination linear independence linear regression loan acceptance logistic basis functions logistic functions machine learning Mallick Markov chain matrix maximum likelihood MCMC methods Metropolis–Hastings model averaging model selection model space multivariate Neal neural network model noninformative prior nonparametric regression normalizing constant number of hidden optimal output overfitting ozone data parameter space plot posterior distribution posterior probability prediction prior distribution Probability of loan radial basis Raftery reference prior response variable Rios Insua Section shrinkage smooth splines standard statistical models step Tibshirani typically variance vector weight decay zero