Pattern recognition and machine learning:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2016
|
| Ausgabe: | softcover reprint of the original 1st edition 2006 |
| Schriftenreihe: | Information science and statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext http://www.springer.com/ Inhaltsverzeichnis |
| Beschreibung: | XX, 738 Seiten |
| ISBN: | 9781493938438 |
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| 245 | 1 | 0 | |a Pattern recognition and machine learning |c Christopher M. Bishop |
| 250 | |a softcover reprint of the original 1st edition 2006 | ||
| 264 | 1 | |a New York, NY |b Springer |c 2016 | |
| 300 | |a XX, 738 Seiten | ||
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| 653 | |a algorithms | ||
| 653 | |a bioinformatics | ||
| 653 | |a classification | ||
| 653 | |a computer vision | ||
| 653 | |a data mining | ||
| 653 | |a learning | ||
| 653 | |a machine learning | ||
| 653 | |a statistics | ||
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Datensatz im Suchindex
| _version_ | 1805076530804555776 |
|---|---|
| adam_text |
Contents Preface vɪɪ Mathematical notation xi Contents 1 Introduction 1.1 Example: Polynomial Curve Fitting. 1.2 Probability Theory. 1.2.1 Probability densities. 1.2.2 Expectations and covariances . 1.2.3 Bayesian probabilities. 1.2.4 The Gaussian distribution . 1.2.5 Curve fitting re-visited. 1.2.6 Bayesian curve fitting . 1.3 Model Selection. 1.4 The Curse of Dimensionality. 1.5 Decision Theory. 1.5.1 Minimizing the misclassification rate . 1.5.2 Minimizing the expected loss . 1.5.3 The reject option. 1.5.4 Inference and decision. 1.5.5 Loss functions for regression. 1.6 Information
Theory. 1.6.1 Relative entropy and mutual information . Exercises . xiii 1 4 12 17 19 21 24 28 30 32 33 38 39 41 42 42 46 48 55 58 xiii
xiv CONTENTS 2 Probability Distributions 67 2.1 Binary Variables. 68 2.1.1 The beta distribution. 71 2.2 Multinomial Variables. 74 2.2.1 The Dirichlet distribution. 76 2.3 The Gaussian Distribution. 78 2.3.1 Conditional Gaussian distributions. 85 2.3.2 Marginal Gaussian distributions. 88 2.3.3 Bayes’ theorem for Gaussian variables. 90 2.3.4 Maximum likelihood for the Gaussian. 93 2.3.5 Sequential estimation. 94 2.3.6 Bayesian inference for the Gaussian. 97 2.3.7 Student’s t-distribution. 102 2.3.8 Periodic variables. 105 2.3.9 Mixtures of Gaussians. 110 2.4 The Exponential Family.113 2.4.1 Maximum likelihood and sufficientstatistics .116 2.4.2 Conjugate priors.
117 2.4.3 Noninformative priors. 117 2.5 Nonparametric Methods. 120 2.5.1 Kernel density estimators. 122 2.5.2 Nearest-neighbour methods .124 Exercises . 127 3 Linear Models for Regression 137 3.1 Linear Basis Function Models. 138 3.1.1 Maximum likelihood and least squares. 140 3.1.2 Geometry of least squares. 143 3.1.3 Sequential learning. 143 3.1.4 Regularized least squares. 144 3.1.5 Multiple outputs . 146 3.2 The Bias-Variance Decomposition. 147 3.3 Bayesian Linear Regression. 152 3.3.1 Parameter distribution. 152 3.3.2 Predictive distribution. 156 3.3.3 Equivalent kernel. 159 3.4 Bayesian Model
Comparison. 161 3.5 The Evidence Approximation. 165 3.5.1 Evaluation of the evidence function. 166 3.5.2 Maximizing the evidence function. 168 3.5.3 Effective number of parameters . 170 3.6 Limitations of Fixed Basis Functions. 172 Exercises . 173
CONTENTS XV 4 Linear Models for Classification 179 4.1 Discriminant Functions. 181 4.1.1 Two classes. 181 4.1.2 Multiple classes. 182 4.1.3 Least squares for classification. 184 4.1.4 Fisher’s linear discriminant. 186 4.1.5 Relation to least squares. 189 4.1.6 Fisher’s discriminant for multiple classes. 191 4.1.7 The perceptron algorithm. 192 4.2 Probabilistic Generative Models. 196 4.2.1 Continuous inputs . 198 4.2.2 Maximum likelihood solution. 200 4.2.3 Discrete features. 202 4.2.4 Exponential family.202 4.3 Probabilistic Discriminative Models. 203 4.3.1 Fixed basis functions. 204 4.3.2 Logistic regression. 205 4.3.3
Iterative reweighted least squares . 207 4.3.4 Multiclass logistic regression. 209 4.3.5 Probit regression. 210 4.3.6 Canonical link functions. 212 4.4 The Laplace Approximation. 213 4.4.1 Model comparison and BIC. 216 4.5 Bayesian Logistic Regression. 217 4.5.1 Laplace approximation. 217 4.5.2 Predictive distribution.218 Exercises. 220 5 Neural Networks 225 5.1 Feed-forward Network Functions. 227 5.1.1 Weight-space symmetries . 231 5.2 Network Training. 232 5.2.1 Parameter optimization.236 5.2.2 Local quadratic approximation. 237 5.2.3 Use of gradient information. 239 5.2.4 Gradient descent optimization. 240 5.3 Error
Backpropagation. 241 5.3.1 Evaluation of error-function derivatives.242 5.3.2 A simple example . 245 5.3.3 Efficiency of backpropagation. 246 5.3.4 The Jacobian matrix.247 5.4 The Hessian Matrix. 249 5.4.1 Diagonal approximation. 250 5.4.2 Outer product approximation. 251 5.4.3 Inverse Hessian. 252
xvi CONTENTS 5.4.4 Finite differences. 252 5.4.5 Exact evaluation of the Hessian . 253 5.4.6 Fast multiplication by the Hessian. 254 5.5 Regularization in Neural Networks . 256 5.5.1 Consistent Gaussian priors. 257 5.5.2 Early stopping . 259 5.5.3 Invariances.261 5.5.4 Tangent propagation. 263 5.5.5 Training with transformed data. 265 5.5.6 Convolutional networks . 267 5.5.7 Soft weight sharing. 269 5.6 Mixture Density Networks. 272 5.7 Bayesian Neural Networks. 277 5.7.1 Posterior parameter distribution. 278 5.7.2 Hyperparameter optimization . 280 5.7.3 Bayesian neural networks for classification. 281 Exercises
. 284 6 Kernel Methods 291 6.1 Dual Representations.293 6.2 Constructing Kernels.294 6.3 Radial Basis Function Networks.299 6.3.1 Nadaraya-Watson model. 301 6.4 Gaussian Processes. 303 6.4.1 Linear regression revisited.304 6.4.2 Gaussian processes for regression.306 6.4.3 Learning the hyperparameters. 311 6.4.4 Automatic relevance determination . 312 6.4.5 Gaussian processes for classification. 313 6.4.6 Laplace approximation. 315 6.4.7 Connection to neural networks. 319 Exercises . 320 7 Sparse Kernel Machines 325 7.1 Maximum Margin Classifiers . 326 7.1.1 Overlapping class distributions. 331
7.1.2 Relation to logistic regression. 336 7.1.3 Multiclass SVMs. 338 7.1.4 SVMs for regression. 339 7.1.5 Computational learning theory.344 7.2 Relevance Vector Machines. 345 7.2.1 RVM for regression. 345 7.2.2 Analysis of sparsity. 349 7.2.3 RVM for classification. 353 Exercises . 357
CONTENTS 8 9 xvii Graphical Models 359 8.1 Bayesian Networks. 360 8.1.1 Example: Polynomial regression. 362 8.1.2 Generative models. 365 8.1.3 Discrete variables. 366 8.1.4 Linear-Gaussian models.370 8.2 Conditional Independence. 372 8.2.1 Three example graphs. 373 8.2.2 D-separation. 378 8.3 Markov Random Fields . 383 8.3.1 Conditional independence properties. 383 8.3.2 Factorization properties .384 8.3.3 Illustration: Image de-noising. 387 8.3.4 Relation to directed graphs. 390 8.4 Inference in Graphical Models. 393 8.4.1 Inference on a chain. 394 8.4.2
Trees. 398 8.4.3 Factor graphs. 399 8.4.4 The sum-product algorithm.402 8.4.5 The max-sum algorithm. 411 8.4.6 Exact inference in general graphs. 416 8.4.7 Loopy belief propagation.417 8.4.8 Learning the graph structure. 418 Exercises . 418 Mixture Models and EM 9.1 423 K-means Clustering. 424 9.1.1 Image segmentation and compression. 428 Mixtures of Gaussians. 430 9.2.1 Maximum likelihood. 432 9.2.2 EM for Gaussian mixtures.435 9.3 An Alternative View of EM. 439 9.3.1 Gaussian mixtures revisited .441 9.3.2 Relation to K-means. 443 9.3.3 Mixtures of Bernoulli
distributions. 444 9.3.4 EM for Bayesian linear regression. 448 9.4 The EM Algorithm in General.450 Exercises . 455 9.2 10 Approximate Inference 461 10.1 Variational Inference. 462 10.1.1 Factorized distributions.464 10.1.2 Properties of factorized approximations. 466 10.1.3 Example: The univariate Gaussian. 470 10.1.4 Model comparison. 473 10.2 Illustration: Variational Mixture of Gaussians. 474
xviii CONTENTS 10.2.1 Variational distribution. 475 10.2.2 Variational lower bound. 481 10.2.3 Predictive density. 482 10.2.4 Determining the number of components. 483 10.2.5 Induced factorizations. 485 10.3 Variational Linear Regression. 486 10.3.1 Variational distribution. 486 10.3.2 Predictive distribution . 488 10.3.3 Lower bound. 489 10.4 Exponential Family Distributions . 490 10.4.1 Variational message passing. 491 10.5 Local Variational Methods. 493 10.6 Variational Logistic Regression. 498 10.6.1 Variational posterior distribution.498 10.6.2 Optimizing the variational parameters. 500 10.6.3 Inference of hyperparameters . 502 10.7 Expectation
Propagation. 505 10.7.1 Example: The clutter problem. 511 10.7.2 Expectation propagation on graphs. 513 Exercises . 517 11 Sampling Methods 523 11.1 Basic Sampling Algorithms.526 11.1.1 Standard distributions . 526 11.1.2 Rejection sampling. 528 11.1.3 Adaptive rejection sampling. 530 11.1.4 Importance sampling. 532 11.1.5 Sampling-importance-resampling.534 11.1.6 Sampling and the EM algorithm.536 11.2 Markov Chain Monte Carlo. 537 11.2.1 Markov chains. 539 11.2.2 The Metropolis-Hastings algorithm. 541 11.3 Gibbs Sampling . 542 11.4 Slice Sampling. 546 11.5 The Hybrid Monte
Carlo Algorithm. 548 11.5.1 Dynamical systems. 548 11.5.2 Hybrid Monte Carlo. 552 11.6 Estimating the Partition Function . 554 Exercises . 556 12 Continuous Latent Variables 559 12.1 Principal Component Analysis. 561 12.1.1 Maximum variance formulation. 561 12.1.2 Minimum-error formulation.563 12.1.3 Applications of PC A. 565 12.1.4 PCA for high-dimensional data . 569
CONTENTS xix 12.2 Probabilistic PCA . 570 12.2.1 Maximum likelihood PCA. 574 12.2.2 EM algorithm for PCA. 577 12.2.3 Bayesian PCA . 580 12.2.4 Factor analysis. 583 12.3 Kernel PCA. 586 12.4 Nonlinear Latent Variable Models. 591 12.4.1 Independent component analysis. 591 12.4.2 Autoassociative neural networks. 592 12.4.3 Modelling nonlinear manifolds. 595 Exercises .599 13 Sequential Data 605 13.1 Markov Models.607 13.2 Hidden Markov Models. 610 13.2.1 Maximum likelihood for the HMM. 615 13.2.2 The forward-backward algorithm . 618 13.2.3 The sum-product algorithm for the HMM. 625
13.2.4 Scaling factors. 627 13.2.5 The Viterbi algorithm.629 13.2.6 Extensions of the hidden Markov model. 631 13.3 Linear Dynamical Systems. 635 13.3.1 Inference in LDS. 638 13.3.2 Learning in LDS. 642 13.3.3 Extensions of LDS.644 13.3.4 Particle filters. 645 Exercises .646 14 Combining Models 653 14.1 Bayesian Model Averaging. 654 14.2 Committees. 655 14.3 Boosting. 657 14.3.1 Minimizing exponential error . 659 14.3.2 Error functions for boosting. 661 14.4 Tree-based Models. 663 14.5 Conditional Mixture
Models. 666 14.5.1 Mixtures of linear regression models. 667 14.5.2 Mixtures of logistic models . 670 14.5.3 Mixtures of experts. 672 Exercises .674 Appendix A Data Sets 677 Appendix B Probability Distributions 685 Appendix C Properties of Matrices 695
xx CONTENTS Appendix D Calculus of Variations 703 Appendix E Lagrange Multipliers 707 References 711 Index 729 |
| any_adam_object | 1 |
| author | Bishop, Christopher M. 1959- |
| author_GND | (DE-588)120454165 |
| author_facet | Bishop, Christopher M. 1959- |
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| discipline | Informatik |
| edition | softcover reprint of the original 1st edition 2006 |
| format | Book |
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| indexdate | 2024-07-20T05:58:46Z |
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| spelling | Bishop, Christopher M. 1959- Verfasser (DE-588)120454165 aut Pattern recognition and machine learning Christopher M. Bishop softcover reprint of the original 1st edition 2006 New York, NY Springer 2016 XX, 738 Seiten txt rdacontent n rdamedia nc rdacarrier Information science and statistics Mustererkennung (DE-588)4040936-3 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf UYQ PBT UYT algorithms bioinformatics classification computer vision data mining learning machine learning statistics Mustererkennung (DE-588)4040936-3 s Maschinelles Lernen (DE-588)4193754-5 s 1\p DE-604 Springer Science + Business Media LLC (DE-588)1065492340 pbl Äquivalent Druck-Ausgabe, Hardcover 978-0-38731-073-2 (DE-604)BV021648269 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=efb4c651772a4ab786a75b8fe8f0f0dd&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com/ Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030197202&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bishop, Christopher M. 1959- Pattern recognition and machine learning Mustererkennung (DE-588)4040936-3 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| subject_GND | (DE-588)4040936-3 (DE-588)4193754-5 |
| title | Pattern recognition and machine learning |
| title_auth | Pattern recognition and machine learning |
| title_exact_search | Pattern recognition and machine learning |
| title_full | Pattern recognition and machine learning Christopher M. Bishop |
| title_fullStr | Pattern recognition and machine learning Christopher M. Bishop |
| title_full_unstemmed | Pattern recognition and machine learning Christopher M. Bishop |
| title_short | Pattern recognition and machine learning |
| title_sort | pattern recognition and machine learning |
| topic | Mustererkennung (DE-588)4040936-3 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | Mustererkennung Maschinelles Lernen |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=efb4c651772a4ab786a75b8fe8f0f0dd&prov=M&dok_var=1&dok_ext=htm http://www.springer.com/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030197202&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bishopchristopherm patternrecognitionandmachinelearning AT springersciencebusinessmediallc patternrecognitionandmachinelearning |