By Herbert K. H. Lee
Bayesian Nonparametrics through Neural Networks is the 1st publication to target neural networks within the context of nonparametric regression and type, operating in the Bayesian paradigm. Its aim is to demystify neural networks, placing them firmly in a statistical context instead of treating them as a black field. This procedure is unlike latest books, which are inclined to deal with neural networks as a computing device studying set of rules rather than a statistical version. as soon as this underlying statistical version is well-known, different normal statistical suggestions might be utilized to enhance the version.
The Bayesian process permits greater accounting for uncertainty. This booklet covers uncertainty in version selection and techniques to house this factor, exploring a couple of rules from records and laptop studying. a close dialogue at the number of previous and new noninformative priors is integrated, besides a considerable literature overview. Written for statisticians utilizing statistical terminology, Bayesian Nonparametrics through Neural Networks will lead statisticians to an elevated realizing of the neural community version and its applicability to real-world difficulties.
To illustrate the foremost mathematical ideas, the writer makes use of examples during the ebook: one on ozone toxins and the opposite on credits functions. The method tested is proper for regression and classification-type difficulties and is of curiosity as a result of frequent power functions of the methodologies defined within the e-book.
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Additional resources for Baysian Nonparametrics via Neural Networks (ASA-SIAM Series on Statistics and Applied Probability)
1). There are two parts to this issue when dealing with neural networks: choosing the set of explanatory variables and choosing the number of hidden nodes. ) First consider choosing an optimal set of explanatory variables. For a given dataset, using more explanatory variables will improve the fit. However, if the variables are not actually relevant, they will not help with prediction. Consider the mean square error for predictions, which has two components—the square of the prediction bias (expected misprediction) and the prediction variance.
The outputs of each layer are taken as the inputs of the next layer. As was proved by several groups, a single layer is all that is necessary to span most spaces of interest, so there is no additional flexibility to be gained by using multiple layers (Cybenko (1989); Funahashi (1989); Hornik, Stinchcombe, and White (1989)). However, sometimes adding layers will give a more compact representation, whereby a complex function can be approximated by a smaller total number of nodes in multiple layers than the number of nodes necessary if only a single layer is used.
In the classical (or frequentist) framework, probabilities are typically interpreted as long-run relative frequencies. Unknown parameters are thought of as fixed quantities, so that there is a "right answer," even if we will never know what it is. The data are used to find a "best guess" for the values of the unknown parameters. Under the Bayesian framework, probabilities are seen as inherently subjective so that, for each person, their probability statements reflect their personal beliefs about the relative likeliness of the possible outcomes.
Baysian Nonparametrics via Neural Networks (ASA-SIAM Series on Statistics and Applied Probability) by Herbert K. H. Lee