Bayesian analysis in natural language processing:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[San Rafael, California]
Morgan & Claypool Publishers
[2019]
|
| Edition: | Second edition |
| Series: | Synthesis lectures on human language technologies
#41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxxi, 311 Seiten Diagramme |
| ISBN: | 9781681735283 9781681735269 |
Staff View
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Record in the Search Index
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| adam_text | List of Figures.......................................................................................................... xix List of Algorithms .................................................................................................. xxi List of Generative Stories ....................................................................................xxiii Preface (First Edition) xxv Acknowledgments (First Edition) ................................................................... xxix Preface (Second Edition)................................................................................... xxxi Preliminaries 1.1 1.2 Probability Measures................................................................................ Random Variables .................................................................................... 1.2.1 Continuous and Discrete Random Variables............................... 1.2.2 Joint Distribution over Multiple Random Variables.................. 1.3 Conditional Distributions........................................................................ 1.3.1 Bayes’Rule .................................................................................... 1.3.2 Independent and Conditionally Independent Random Variables 1.3.3 Exchangeable Random Variables................................................. 1.4 1.5 Expectations of Random Variables.......................................................... Models....................................................................................................... 1.5.1 Parametric vs. Nonparametric
Models......................................... 1.5.2 Inierence with Models .................................................................. 1.5.3 Generative Models........................................................................ 1.5.4 Independence Assumptions in Models......................................... 1.5.5 Directed Graphical Models ......................................................... Learning from Data Scenarios.................................................................. 1.6 1.7 1.8 1.9 Bayesian and Frequentisi Philosophy (Tip of the Iceberg).................... Summary ................................................................................................... Exercises..................................................................................................... 1 1 2 о A 4 5 6 7 8 9 11 11 12 14 16 17 19 22 23 24
Introduction 25 2.1 2.2 Overview: Where Bayesian Statistics and NIP Meet................ First Example: ΊЪс Latent Dirichlet Allocation Alodel.............. 2.2.1 The Dirichlet Distribution ................................................. 2.2.2 Inference.............................................................................. 2.2.3 Summan՜.............................................................................. 26 2.3 2.Վ Second Example: Bayesian Text Regression................................. Conclusion and Summary.............................................................. 40 41 2.5 Exercises........................................................................................... 42 Priors......................................................................................................... 43 3.1 Conjugate Priors.............................................................................. 3.1.1 Conjugate Priors and Normalization Constants.............. 3.1.2 The Use oí Conjugate Priors with Patent Variable ModeP 3.1.3 Mixture of Conjugate Priors............................................... 3.1.Վ Renormalized Conjugate Distributions............................. 3.1.5 Discussion: To Be or not to Be Conjugate?....................... 3.1.6 Summary.............................................................................. Priors Over Multinomial and Categorical Distributions............ 3.2.1 The Dirichlet Distribution Re-Visited............................... 3.2.2 The Logistic Normal Distribution..................................... 3.2.3
Discussion............................................................................ 3.2.Վ Summarv.............................................................................. 44 47 Non-Informative Priors.................................................................. 3.3.1 Uniform and Improper Priors............................................. 3.3.2 Jeflrevs Prior........................................................................ 3.3.3 Discussion............................................................................ 66 3.2 3.3 3.4 Conjugacvand Exponential Models............................................. 3.5 Multiple Parameter Draws in Models........................................... 3.6 3.7 Structural Priors.............................................................................. Conclusion and Summary.............................................................. 3.8 Exercises.......................................................................................... 30 34 36 36 50 51 S.1 xO 6~ 6s 67 os 60 60 t S Bavesian Estimation.......................................................................................................77 4.1 Learning with Latent Variables: Two Views........................................................ 75 4.2 Bavesian Point Estimation.................................................................................. /0
ХНІ 4.2.1 Maximum a Posteriori Estimation............................................................79 4.2.2 Posterior Approximations Based on the MAP Solution.........................87 4.2.3 Deeision-lheoretic Point Estimation........................................................89 4.2.4 Discussion and Summary........................... 90 5 4.3 4.4 Empirical Bayes.....................................................................................................90 Asymptotic Behavior of the Posterior..................................................................93 4.5 Summary ............................................................................................................... 93 4.6 Exercises................................................................................................................. 95 Sampling Methods........................................................................................... 97 5.1 MC MC Algorithms: Overview............................................................................ 98 5.2 NEP Model Structure tor MCMC Inference..................................................... 99 5.2.1 Partitioning the Latent Variables............................................................100 5.3 Gibbs 5.3.1 5.3.2 5.3.3 5.3.4 5.4 lhe Metropolis-Hastings Algorithm.............................................................. 113 5.4.1 Variants of Metropolis-Hastings............................................................114 5.5 Slice
Sampling..................................................................................................... Ю 5.5.1 Auxiliary Variable Sampling.................................................................... 117 5.5.2 dite Use of Slice Sampling and Auxiliary Variable Sampling in NLP. 117 5.6 Simulated Annealing................................. 5.7 Convergence of MCMC Algorithms................................................................ 119 5.8 5.9 Markov Chain: Basic Iheory...............................................................................121 Sampling Algorithms Not in the MCMC Realm ........................................... 123 5.10 Monte Carlo Integration.....................................................................................126 Sampling................................................................................................... 101 Collapsed Gibbs Sampling...................................................................... 105 Operator View...........................................................................................109 Parallelizing the Gibbs Sampler.............................................................. Ill Summary...................................................................................................112 118 5.11 Discussion.............................................................................................................. 127 5.11.1 Computability of Distribution vs. Sampling......................................... 127 5.11.2 Nested MCMC
Sampling...................................................................... 128 5.11.3 Runtime ol MCMC Samplers................................................................ 128 5.11.4 Particle Filtering.......................................................................................128 5.12 Conclusion and Summary.................................................................................. 130 5.13 Exercises............................................................................................................... 132
xiv 6 7 Variational Inference................................................................................................. 135 6.1 Variational Bound on Marginal Log-Likelihood........................................... 135 6.2 6.3 Mean-Field Approximation............................................................................... 13H .Mean-Field Variational Inference Algorithm.................................................. 139 6.3.1 Dirichlet-Multinomial Variational Inference....................................... 14] 6.3.2 Connection to the Expectation-Maximization Algorithm................... 145 6.4 6.5 Empirical Baves with Variational inference .................................................... Discussion........................................................................................................... 6.5.1 Initialization of the Inference Algorithms........................................... 6.5.2 Convergence Diagnosis.......................................................................... 6.5.3 The Use of Variational Inference for Decoding................................... 6.5.4 Variational Inference as KL Divergence Minimization....................... 6.5.5 Online Variational inference.................................................................. 6.6 Summary ........................................................................................................... 152 6.7 Exercises............................................................................................................. 153 147 48 148 149 150 151 15] Nonparametric
Priors...................................................................................................155 7.1 7.2 Tlie Dirichlet Process: fhree Views.................................................................. 7.1.1 ihe Stick-Breaking Process .................................................................. 7.1.2 Ihe Chinese Restaurant Process............................................................ Dirichlet Process Mixtures................................................................................. 7.2.1 Inference with Dirichlet Process Mixtures........................................... 7.2.2 Dirichlet Process Mixture as a Limit of Mixture Models................... 156 157 159 101 161 165 7.3 Hie Hierarchical Dirichlet Process .................................................................. 165 7.4 Hie Pittmn-Yor Process..................................................................................... 16H 7.4.1 Pitman-Yor Process forLanguage Modeling......................................... 169 7.4.2 Power-Law Behavior of the Pitman-Yor Process................................. 170 7.5 Discussion. 7.5.1 Gaussian Processes............................................... 7.5.2 ihe Indian Bullet Process..................................... 7.5.3 Nested Chinese Restaurant Process..................... 7.5.4 Distance-Dependent Chinese Restaurant Process 7.5.5 Sequence Memoizers ........................................... 1 /2 7.6 Summary .......................................................................... 175 7.7 Exercises 1/6
XV 8 Bayesian Grammar Models...................................................................................177 Я.1 Bayesian Midden Markov Models..................................................................... 178 8.1.1 Midden Markov Models with an Infinite State Space.........................179 8.2 Probabilistic Context-Free Grammars................................................................ 181 8.2.1 PCFGs as a Collection of Multinomials............................................. 184 8.2.2 Basic Inference Algorithms for PCFGs............................................... 185 8.2.3 Mídden Markov Models as PCFGs..................................................... 189 8.3 Bayesian Probabilistic Context-Free Grammars................................................189 8.3.1 Priors on PCFGs.......................................................................................189 8.3.2 Monte Carlo Inference with Bayesian PCFGs ...................................190 8.3.3 Variational Inference with Bayesian PCFGs.......................................192 Adaptor Grammars ............................................................................................. 193 8.4.1 Pitman-Yor Adaptor Grammars.............................................................. 194 8.4.2 Stick-Breaking View of PYAG................................................................ 196 8.4.3 Inference with PYAG...............................................................................198 1 lierarchical Dirichlet Process PCl’Gs (MDP-PCFGs) .................................200
8.5.1 Extensions to the MDP-PCFG Model............................................... 201 Dependency Grammars.................................................................................... 202 8.6.1 State-Split Nonparametric Dependency Models...................................203 Synchronous Grammars...................................................................................... 205 Multilingual 1,earning.........................................................................................206 8.8.1 PatT-ol -Speech Fagging..........................................................................206 8.8.2 Grammar Induction ................................................................................ 208 8.4 8.5 8.6 8.7 8.8 8.9 8.10 Further Reading...................................................................................................209 Summary ............................................................................................................. 211 8.11 Exercises.................................................................................................................212 9 Representation Learning and Neural Networks................................................213 9.1 9.2 Neural Networks and Representation Learning: Why Now?...........................214 Word Embeddings...............................................................................................217 9.2.1 Skip-Gram Models for Word Embeddings........................................... 218 9.2.2 Bayesian Skip-Gram Word
Embeddings............................................... 220 9.2.3 Discussion.................................................................................................221 9.3 Neural Networks ...............................................................................................222 9.3.1 Frequentisi Estimation and the Backpropagation Algorithm.............. 225 9.3.2 Priors on Neural Network Weights ........................................................228
XVÏ 9.4 9.5 Modern Use of Neural Networks in NLP.......................................................... 250 9.4.1 Recurrent and Recursive Neural Networks .............................................. 250 9.4.2 Vanishing and Exploding Gradient Problem............................................ 252 9.4.3 Neural Encoder-Decoder Models ............................................................ 255 9.4.4 Convolutional Neural Networks..................................................................254 242 runing Neural Networks.............................. 9.5.1 Regularization.................................... 9.5.2 Hvperparameter Tuning................... 9.6 Generative Modeling with Neural Networks 9.6.1 Variational Autoencoders................. 9.6.2 Generative Adversarial Networks . . . 9.7 Conclusion..................................................... 9.8 Exorcises.......................................................... 24 1 244 246 252 254 25o Closing Remarks ............................................................................................................257 Basic Concepts................................................................................................................. 259 Л.1 Basic Concepts in Information lheorv..................................................................254 A.1.1 Entropy and Cross Entropy....................................................................... 2M A.1.2 Kailllrack-Eeibler Divergence.....................................................................260 В Л.2 Other Basic Concepts
...........................................................................................260 A.2.1 Jensen’s Inequality.........................................................................................MU A.2.2 Tie Chain Rule lor Diflercntiation ........................................................261 A.2.3 Transformation ot Continuous Random Variables .............................. 261 Л.2.4 The Expectation-Maximization Algorithm............................................. 2(42 A.3 Basic Concepts in Optimization............................................................................ 2 4 A.3.1 Stochastic Gradient Descent ......................................................................2o4 A.3.2 Constrained Optimization......................................................................... 2 5 Distribution Catalog...................................... .............................................................267 B.1 The Multinomial Distribution..............................................................................2(l- B.2 Ihe Dirichlet Distribution.................................................................................... 2oS B.3 Tie Poisson Distribution.......................................................................................2i B.4 B.5 Tie Gamma Distribution........................................................................................-64 Tie Multivariate Normal Distribution ............................................................... 2/0 B.6 Tie Laplace
Distribution.......................................................................................2 0 271 Tie Logistic Normal Distribution B.7
xvii ii.H U.Ч lhc Inverse Wishart Distribution.................................................................. 272 lhe Gumbel Distribution ..............................................................................273 Bibliography........................................................................................................... 275 Authors Biography.................................................................................................305 index ....................................................................................................................... 307
|
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| indexdate | 2024-07-10T08:29:03Z |
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| series | Synthesis lectures on human language technologies |
| series2 | Synthesis lectures on human language technologies |
| spelling | Cohen, Shay Verfasser (DE-588)1108783767 aut Bayesian analysis in natural language processing Shay Cohen (University of Edinburgh) Second edition [San Rafael, California] Morgan & Claypool Publishers [2019] © 2019 xxxi, 311 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Synthesis lectures on human language technologies #41 Sprachverarbeitung (DE-588)4116579-2 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 s Sprachverarbeitung (DE-588)4116579-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-68173-527-6 Erscheint auch als Online-Ausgabe, epub 978-1-68173-529-0 Synthesis lectures on human language technologies #41 (DE-604)BV035447238 41 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031256494&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cohen, Shay Bayesian analysis in natural language processing Synthesis lectures on human language technologies Sprachverarbeitung (DE-588)4116579-2 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| subject_GND | (DE-588)4116579-2 (DE-588)4204326-8 |
| title | Bayesian analysis in natural language processing |
| title_auth | Bayesian analysis in natural language processing |
| title_exact_search | Bayesian analysis in natural language processing |
| title_full | Bayesian analysis in natural language processing Shay Cohen (University of Edinburgh) |
| title_fullStr | Bayesian analysis in natural language processing Shay Cohen (University of Edinburgh) |
| title_full_unstemmed | Bayesian analysis in natural language processing Shay Cohen (University of Edinburgh) |
| title_short | Bayesian analysis in natural language processing |
| title_sort | bayesian analysis in natural language processing |
| topic | Sprachverarbeitung (DE-588)4116579-2 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| topic_facet | Sprachverarbeitung Bayes-Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031256494&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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