LEADER 05295nam 22006615 450 001 9910478911203321 005 20200705223411.0 010 $a1-4612-0745-2 024 7 $a10.1007/978-1-4612-0745-0 035 $a(CKB)3400000000089253 035 $a(SSID)ssj0000805284 035 $a(PQKBManifestationID)11517483 035 $a(PQKBTitleCode)TC0000805284 035 $a(PQKBWorkID)10837065 035 $a(PQKB)10180800 035 $a(DE-He213)978-1-4612-0745-0 035 $a(MiAaPQ)EBC3074890 035 $a(PPN)238007030 035 $a(EXLCZ)993400000000089253 100 $a20121227d1996 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBayesian Learning for Neural Networks$b[electronic resource] /$fby Radford M. Neal 205 $a1st ed. 1996. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1996. 215 $a1 online resource (204 p.) 225 1 $aLecture Notes in Statistics,$x0930-0325 ;$v118 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-94724-8 320 $aIncludes bibliographical references and index. 327 $a1 Introduction -- 1.1 Bayesian and frequentist views of learning -- 1.2 Bayesian neural networks -- 1.3 Markov chain Monte Carlo methods -- 1.4 Outline of the remainder of the book -- 2 Priors for Infinite Networks -- 2.1 Priors converging to Gaussian processes -- 2.2 Priors converging to non-Gaussian stable processes -- 2.3 Priors for nets with more than one hidden layer -- 2.4 Hierarchical models -- 3 Monte Carlo Implementation -- 3.1 The hybrid Monte Carlo algorithm -- 3.2 An implementation of Bayesian neural network learning -- 3.3 A demonstration of the hybrid Monte Carlo implementation -- 3.4 Comparison of hybrid Monte Carlo with other methods -- 3.5 Variants of hybrid Monte Carlo -- 4 Evaluation of Neural Network Models -- 4.1 Network architectures, priors, and training procedures -- 4.2 Tests of the behaviour of large networks -- 4.3 Tests of Automatic Relevance Determination -- 4.4 Tests of Bayesian models on real data sets -- 5 Conclusions and Further Work -- 5.1 Priors for complex models -- 5.2 Hierarchical Models ? ARD and beyond -- 5.3 Implementation using hybrid Monte Carlo -- 5.4 Evaluating performance on realistic problems -- A Details of the Implementation -- A.1 Specifications -- A.1.1 Network architecture -- A.1.2 Data models -- A.1.3 Prior distributions for parameters and hyperparameters -- A.1.4 Scaling of priors -- A.2 Conditional distributions for hyperparameters -- A.2.1 Lowest-level conditional distributions -- A.2.2 Higher-level conditional distributions -- A.3 Calculation of derivatives -- A.3.1 Derivatives of the log prior density -- A.3.2 Log likelihood derivatives with respect to unit values -- A.3.3 Log likelihood derivatives with respect to parameters -- A.4 Heuristic choice of stepsizes -- A.5 Rejection sampling from the prior -- B Obtaining the software. 330 $aArtificial "neural networks" are widely used as flexible models for classification and regression applications, but questions remain about how the power of these models can be safely exploited when training data is limited. This book demonstrates how Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional training methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. A practical implementation of Bayesian neural network learning using Markov chain Monte Carlo methods is also described, and software for it is freely available over the Internet. Presupposing only basic knowledge of probability and statistics, this book should be of interest to researchers in statistics, engineering, and artificial intelligence. 410 0$aLecture Notes in Statistics,$x0930-0325 ;$v118 606 $aProbabilities 606 $aStatistics  606 $aArtificial intelligence 606 $aComputer simulation 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/S17020 606 $aArtificial Intelligence$3https://scigraph.springernature.com/ontologies/product-market-codes/I21000 606 $aSimulation and Modeling$3https://scigraph.springernature.com/ontologies/product-market-codes/I19000 615 0$aProbabilities. 615 0$aStatistics . 615 0$aArtificial intelligence. 615 0$aComputer simulation. 615 14$aProbability Theory and Stochastic Processes. 615 24$aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 615 24$aArtificial Intelligence. 615 24$aSimulation and Modeling. 676 $a006.3 700 $aNeal$b Radford M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0116958 906 $aBOOK 912 $a9910478911203321 996 $aBayesian learning for neural networks$982541 997 $aUNINA