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In order to understand the nature of semi-supervised learning, it will be useful first to take a look at supervised and unsupervised learning.
Adaptive Computation and Machine Learning Thomas dietterich editor Christopher Bishop, David Heckerman, Michael Jordan, and Michael Kearns, As te editors Bioinformatics: The Machine Learning Approach, Pierre Baldi and Soren Brunak Reinforcement Learning: An Introduction, Richard s Sutton and Andrew G. Barto Graphical Models for Machine learning and Digital Communication, Brendan J F Learning in graphical Models, Michael I. Jordan Causation, Prediction, and Search, second edition, Peter Spirtes, Clark glymour and richard scheines Principles of Data Mining, David Hand, Heikki Mannila, and Padhraic Smyth Bioinformatics: The Machine Learning Approach, second edition, Pierre Baldi and Soren brunak Learning Kernel Classifiers: Theory and algorithms, Ralf Herbrich Learning with Kernels: Support vector Machines, Regularization, Optimization, and Beyond, Bernhard Scholkopf and Alexander J Smola Introduction to Machine Learning, Ethem Alpaydin Gaussian processes for Machine Learning, Carl Edward Rasmussen and Christo- pher k.I. Williams Semi-Supervised Learning, Olivier Chapelle, Bernhard Scholkopf, and Alexander Zien Semi-Supervised Learning Olivier Chapelle Bernhard scholkopf Alexander zien The mit Press Cambridge, Massachusetts London, england C2006 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means(including photocopying, recording, or information storage and retrieval without permission in writing from the publisher Typeset by the authors using IATEX 2 Printed and bound in the United States of America Library of Congress Cataloging-in-Publication Data Semi-supervised learning/ edited by Olivier Chapelle, Bernhard Scholkopf, Alexander Zien p cm-(Adaptive computation and machine learning Includes bibliographical references ISBN978-0-262-03358-9(alk. paper Supervised learning(Machine learning)I Chapelle, Olivier. II. Scholkopf, Bernhard. III. Zien Alexander, IV. s Q325.75422006 006.31dc22 2006044448 10987654321 Contents Series foreword Preface X11 1 Introduction to Semi-Supervised Learning 1 1.1 Supervised, Unsupervised, and Semi-Supervised Learning 1. 2 When Can Semi-Supervised Learning Work? 4 1. 3 Classes of Algorithms and Organization of This Book Generative Models 13 2 a Taxonomy for semi-Supervised Learning Methods 15 Matthias seeger 2.1 The Semi-Supervised Learning Problem 15 2.2 Paradigms for Semi-Supervised learning 17 2.3 Examples 22 2. 4 Conclusions 31 3 Semi-Supervised Text Classification Using EM 33 Kamal Nigam, Andrew McCallum, Tom Mitchell 3.1 Introduction 33 3.2 A Generative Model for Text 35 3.3 Experimental Results with Basic EM 41 3.4 USing a More Expressive Generative Model 43 3.5 Overcoming the Challenges of Local Maxima 49 3.6 Conclusions and summary 54 4 Risks of Semi-Supervised Learning 57 Fabio cozman. ra Cohen 4.1 Do Unlabeled Data Improve or Degrade Classification Performance? 57 4.2 Understanding Unlabeled Data: Asymptotic Bias 59 4.3 The Asymptotic Analysis of Generative Semi-Supervised Learning 63 4.4 The value of labeled and unlabeled data ......67 4.5 Finite Sample effects Contents 4.6 Model Search and robustness 70 4.7 Conclusion 5 Probabilistic Semi-Supervised Clustering with Constraints 73 Sugato Basu, Mikhail Bilenko, Arindam Banerjee, Raymond Mooney 5.1I 74 5.2 HMRF Model for Semi-Supervised Clustering 5.3 HMRF-KMEANS Algorithm 81 5.4 Active Learning for Constraint Acquisition 93 5.5 Experimental results 5.6 Related Work 100 5.7 Conclusions 101 Low-Density Separation 103 6 Transductive Support vector Machines 105 Thorsten oachims 6.1 Introduction .105 6.2 Transductive Support Vector Machines 108 6.3 Why Use Margin on the Test Set? 6.4 Experiments and Applications of Tsvms 112 6.5 Solving the tsVM Optimization Problem 114 6.6 Connection to Related approaches 116 6.7 Summary and conclusions 116 7 Semi-Supervised Learning Using Semi-Definite Programming 119 Tiil De bie, Nello Cristianini 7.1 Relaxing svm transduction 7.2 An Approximation for Speedup 126 7.3 General Semi-Supervised Learning Settings 128 7.4 Empirical results 129 7.5 Summary and Outlook 133 Appendix: The Extended Schur Complement Lemma 134 8 Gaussian Processes and the Null-Category Noise Model 137 Neil D. lawrence. Michael l. jordan 8.1 Introduction 137 8.2 The noise model 141 8.3 Process Model and Effect of the Null-Category ..143 8.4 Posterior Inference and Prediction 145 8.5 Result 147 8.6 Discussion 149 9 Entropy Regularization 151 ontents Yves grandvalet, Yoshua bengio 9.1 Introduction 151 9.2 Derivation of the Criterion 2 9.3 Opt Imlzaulon algorithms 155 9. 4 Related methods 158 9.5 Experiments 160 9. 6 Conclusion 166 Appendix: Proof of Theorem 9.1 166 10 Data-Dependent regularization 169 Adrian Corduneanu, Tommi Jaakkola 10.1 Introduction 169 10.2 Information Regularization on Metric Spaces .174 10.3 Information Regularization and Relational data 182 10.4 Discussion 189 II Graph-Based Methods 191 11 Label Propagation and Quadratic Criterion 193 Yoshua Bengio, Olivier Delalleau, Nicolas Le rou.C 11.1 Introduction 193 11.2 Label Propagation on a similarity graph 194 11.3 Quadratic Cost Criterion 198 11. 4 From transduction to induction 205 11.5 Incorporating Class Prior Knowledge 205 11.6 Curse of Dimensionality for Semi-Supervised Learning 11. 7 Discussion 215 12 The Geometric Basis of Semi-Supervised Learning 217 Vikas sindhwani, Misha Belkin, Partha Niyoga 12. 1 Introduction 217 12.2 Incorporating Geometry in Regularization .220 12.3 Algorithms 224 12.4 Data-Dependent Kernels for Semi-Supervised Learning 229 12.5 Linear Methods for Large-Scale semi-Supervised Learning 231 12.6 Connections to Other Algorithms and Related Work 232 12. 7 Future Directions 234 13 Discrete Regularization 237 Denggong Zhou, Bernhard Scholkopf 13.1 Introduction 237 13.2 Discrete Analysis 13.3 Discrete Regularization .245 13.4 Conclusion 249 Contents 14 Semi-Supervised Learning with Conditional Harmonic Mixing 251 Christopher C. Burges, John C. Platt 14.1 Introduction 251 14.2 Conditional Harmonic mixing 255 14.3 Learning in CHM Models 256 14.4 Incorporating Prior Knowledge 261 14.5 Learning the Conditionals 261 14.6 Model averaging 262 14.7 Experiments 263 14.8 Conclusions V Change of Representation 275 15 Graph Kernels by spectral Transforms 277 Xiaojin Zhu, Jaz Kandola, John Lafferty, Zoubin ghahramani 15.1 The Graph Laplacian 278 15.2 Kernels by Spectral transforms 280 15.3 Kernel Alignment 281 15.4 Optimizing Alignment Using QCQP for Semi-Supervised Learning 282 15.5 Semi-Supervised Kernels with Order Constraints 283 15.6 Experimental results 15.7 Conclusion 16 Spectral Methods for Dimensionality Reduction 293 Lawrence k. saul, Kilian Q. Weinberger, Fei Sha, Jihun Ham, Daniel D. Lee 16. 1 Introduction 293 16.2 Linear Methods 16.3 Graph-Based Methods 297 16.4 Kernel Methods ..303 16.5 Discussion 306 17 Modifying Distances 309 Sajama, Alon Orlitsky 17.1 Introduction 309 17.2 Estimating dbd metrics 312 17.3 Computing DBD Metrics 321 17.4 Semi-Supervised Learning Using Density-Based Metrics 327 17.5 Conclusions and Future Work .329 V Semi-Supervised learning in Practice 331 18 Large-Scale Algorithms 333 Contents Olivier Delalleau, Yoshua Bengio, Nicolas Le rou 18.1 Introduction 333 18.2 Cost Approximations 334 18.3 Subset Selection 337 18.4 Discussion 340 19 Semi-Supervised Protein Classification Using Cluster Kernels 343 Jason weston, Christina leslie, Eugene le, William stafford noble 19.1 Introduction 343 19.2 Representations and Kernels for Protein Se 345 19.3 Semi-Supervised Kernels for Protein Sequences 348 19.4 Experiments .352 19.5 Discussion 358 20 Prediction of Protein function from Networks 361 Hyunyung Shin, Koji tsuda 20.1 Introduction 20.2 Graph-Based Semi-Supervised learning 364 20.3 Combining Multiple graphs 20.4 Experiments on Function Prediction of Proteins 369 20.5 Conclusion and Outlook 374 21 Analysis of Benchmarks 377 21.1 The benchmark 377 21.2 Application of SsL Methods 383 21.3 Results and discussion 390 ⅵ I Perspectives 395 22 An Augmented PAC Model for Semi-Supervised Learning 397 Maria-Flo Balcan. aurim blum 22.1 Introduction 22. A Formal Framework 400 22.3 Sample complexity results .403 22.4 Algorithmic Results 412 22.5 Related models and discussion ..416 23 Metric-Based Approaches for Semi- Supervised Regression and Classification 421 Dale schuurmans, Finnegan Southey, Dana wilkinson, Yuhong guo 23. 1 Introductio 421 23.2 Metric Structure of Supervised Learning 423

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