Bayesian approach for neural networks--review and case studies

Neural Networks : the Official Journal of the International Neural Network Society
J Lampinen, A Vehtari

Abstract

We give a short review on the Bayesian approach for neural network learning and demonstrate the advantages of the approach in three real applications. We discuss the Bayesian approach with emphasis on the role of prior knowledge in Bayesian models and in classical error minimization approaches. The generalization capability of a statistical model, classical or Bayesian, is ultimately based on the prior assumptions. The Bayesian approach permits propagation of uncertainty in quantities which are unknown to other assumptions in the model, which may be more generally valid or easier to guess in the problem. The case problem studied in this paper include a regression, a classification, and an inverse problem. In the most thoroughly analyzed regression problem, the best models were those with less restrictive priors. This emphasizes the major advantage of the Bayesian approach, that we are not forced to guess attributes that are unknown, such as the number of degrees of freedom in the model, non-linearity of the model with respect to each input variable, or the exact form for the distribution of the model residuals.

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Citations

Jul 16, 2010·Health Care Management Science·Jaakko RiihimäkiAki Vehtari
Oct 25, 2002·Neural Computation·Aki Vehtari, Jouko Lampinen
Nov 30, 2007·Neural Computation·Tatiana MiazhynskaiaGeorg Dorffner
Dec 22, 2009·Neural Networks : the Official Journal of the International Neural Network Society·Henrique S Hippert, James W Taylor
Mar 11, 2006·IEEE Transactions on Neural Networks·Vivien Rossi, Jean-Pierre Vila
Aug 24, 2010·IEEE Transactions on Neural Networks·Fei ChengHuilin Xiong
Sep 25, 2004·IEEE Transactions on Neural Networks·Wei ChuChong Jin Ong
Apr 4, 2006·Neural Networks : the Official Journal of the International Neural Network Society·Udo V ToussaintVolker Dose
Jan 23, 2008·Biostatistics·Martyn Plummer
Jan 1, 2013·G3 : Genes - Genomes - Genetics·Paulino Pérez-RodríguezSusanne Dreisigacker
Sep 16, 2019·Molecular Neurobiology·Jerónimo AuzmendiAlberto Javier Ramos
Oct 23, 2017·The Journal of Chemical Physics·Olli-Pekka KoistinenHannes Jónsson
Nov 19, 2009·Scandinavian Journal of Surgery : SJS : Official Organ for the Finnish Surgical Society and the Scandinavian Surgical Society·R SundU Häkkinen
Feb 20, 2021·Neural Networks : the Official Journal of the International Neural Network Society·Shrijita Bhattacharya, Tapabrata Maiti
Apr 30, 2010·Analytical Chemistry·Grady Hanrahan
Nov 29, 2005·Journal of Chemical Information and Modeling·Michael FernándezJulio Caballero

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