Deep Learning 2016

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Deep Learning 2016 Ian Goodfellow, Yoshua Bengio, Aaron Courville
CONTENTS 3.2 Random Variables 56 3.3 Probability distributions 56 3.4 Marginal Probability 3.5 Conditional Probability 59 3. 6 The chain rule of conditional Probabilities 59 3.7 Independence and Conditional Independence 60 3.8 Expectation, Variance and Covariance 60 3.9 Common Probability Distributions 62 3.10 Useful Properties of Common Functions 67 3.11 Bayes' Rule 70 3.12 Technical Details of continuous variables 71 3.13 Information Theory 72 3.14 Structured Probabilistic models 75 4 Numerical Computation 80 4. 1 Overflow and Underflow 4.2 Poor Conditioning 4.3 Gradient-Based OptiInization 022 4.4 Constrained Optimization 93 4.5 Example: Linear Least Squares 96 5 Machine learning basics 98 Learning Algorithms 99 5. 2 Capacity, Overfitting and Underfitting 5.3 Hyperparameters and Validation Sets .120 5.1 Estimators Bias and Variance 122 5.5 Maximum likelihood estimation 131 5.6 Bayesian Statistics .135 5.7 Supervised Learning Algorithms 5.8 Unsupervised Learning Algorithms 145 5.9 Stochastic gradient Descent 150 5.10 Building a Machine Learning Algorithm 152 5.11 Challenges Motivating Deep Learning 154 II Deep Networks: Modern Practices 165 6 Deep Feedforward Networks 167 6.1 Example: Learning XOR 170 6.2 Gradient-Based Learning 176 CONTENTS 6.3 Hiddon units ..190 6.4 Architecture de esion 196 6.5 Back-Propagation and Other Differentiation Algorithms 203 6.6 Historical notes 224 7 Regularization for Deep Learning 228 7.1 Parameter Norm Penalties 7.2 Norm Penalties as Constrained Optimization 237 7.3 Regularization and under-Constrained problems Q 7. 4 Dataset Augmentation 240 7.5 Noise Robustness 242 7.6 Semi-Supervised Learning 243 7.7 Multi- Task Learning .214 7.8 Early Stopping 246 7.9 Parameter Tying and Parameter Sharing .253 7.10 Sparse Representations .254 7. 11 Bagging and Other Ensemble Methods .,,256 7.12 Dropout 258 7. 13 Adversarial Trainin 268 7.14 Tangent Distance, Tangent Prop, and Manifold Tangent Classifier 270 8 Optimization for Training Deep Models 274 8. 1 How Learning Differs from Pure Optimization 275 8.2 Challenges in Neural Network Optimization .282 8.3 Basic algorithms 294 8.1 Parameter Initialization Strategies 30l 8.5 Algorithms with Adaptive Learning rates 306 8.6 Approximate Second-Order Methods 310 8.7 Optimization Strategies and Meta-algorithms 317 9 Convolutional nctworks 330 9.1 The Convolution Operation .331 9.2 Motivation .335 9.3 Pooling 339 9.4 Convolution and Pooling as an Infinitely Strong Prior .345 9.5 Variants of the basic convolution Function 347 9.6 Structured Outputs 358 9. 7 Data Types 360 9.8 Efficient Convolution Algorithms ..362 9.9 Random or Unsupervised Features 363 CONTENTS 9.10 The Ncuroscicntific Basis for Convolutional Nctworks ..364 9. 11 Convolutional Networks and the History of Deep Learning 371 10 Sequence Modeling: Recurrent and Recursive Nets 373 10.1 Unfolding Computational graphs 10.2 Recurrent Neural Networks 378 10.3 Bidirectional rnns .395 10.4 Encoder-Decoder Sequence-to-Sequence Architectures .396 10.5 Deep Recurrent Networks a8 10.6 Recursive Neural Networks 10.7 The Challenge of Long- Term Dependencies .402 10.8 Echo State Networks 405 10.9 Leaky Units and Other Strategies for Multiple Time Scales 10.10 The Long Short-Term Memory and Other Gated RNNS 410 10.11 Optimization for Long-Term Dependencies .414 10.12 Explicit Memory 418 11 Practical Methodology 423 11.1 Performance Metrics .,424 11.2 Default baseline models 427 11.3 Determining Whether to Gather More Data .,,428 11.4 Selecting Hyperparameters .429 11.5 Debugging Strategies 438 11.6 Example: Multi-Digit Number recognition 442 12 Applications 445 12.1 Large Scale Deep Learning .445 12.2 Computer Vision 454 12.3 Speech Recognition 460 12.4 Natural Language Processing 463 12.5 Other Applications 479 III Deep Learning Research 488 13 Linear Factor Models 491 13.1 Probabilistic PCA and Factor Analysis 492 13.2 Independent Component Analysis(ICA) 493 13.3 Slow Feature Analysis 495 13.1 Sparse Coding .498 CONTENTS 13.5 Manifold Interprctation of PCA .501 14 Autoencoders 504 14.1 Undercomplete Autoencoders 505 14.2 Regularized Autoencoders 506 11.3 Representational Power, Layer Size and Depth 510 14.4 Stochastic Encoders and decoders 511 14.5 Denoising Autoencoders .512 14.6 Learning Manifolds with Autoencoders 517 14.7 Contractive Autoencoders 523 14.8 Predictive Sparse Decomposition .525 14.9 Applications of Autoencoders 526 15 Representation Learning 528 15.1 Greedy Layer-Wise Unsupervised Pretraining .5:30 15.2 Transfer Learning and Domain Adaptation .538 15.3 Semi-Supervised Disentangling of Causal Factors 543 15.4 Distributed Representation 548 15.5 Exponential Gains from Depth .555 15.6 Providing Clues to Discover Underlying Causes 556 16 Structured Probabilistic Models for Deep Learning 560 16.1 The Challenge of Unstructured Modeling .56l 16.2 Using Graphs to Describe Model Structure............. 565 16.3 Sampling from Graphical Models 582 16.4 Advantages of Structured Modeling 584 16.5 Learning about Dependencies 16.6 Inference and Approximate Inference 16.7 The Deep Learning Approach to Structured Probabilistic Models 586 17 Monte Carlo methods 592 17.1 Sampling and Monte Carlo Methods 592 17.2 Importance Sampling .594 17.3 Markov Chain Monte Carlo Methods 597 17.4 Gibbs sampling 601 17. The Challenge of mixing between Separated Modes 601 18 Confronting the Partition Function 607 18.1 The Log-Likelihood Gradient .608 18.2 Stochastic Maximum Likelihood and Contrastive Divergence... 609 CONTENTS 18.3 Pscudolikclihood ..617 18.4 Score Matching and Ratio Matching .619 18.5 Denoising Score Matching 621 18.6 Noise-Contrastive Estimation 622 18.7 Estimating the Partition Function 625 19 Approximate Inference 633 19.1 Inference as Optimization 19.2 Expectation Maximization 636 19.3 MAP Inference and Sparse Coding 637 19.4 Variational Inference and Learning .640 19.5 Learned Approximate Inference 653 20 Deep Generative Models 656 20.1 Boltzmann Machines 656 20.2 Restricted boltzmann machines .658 20.3 Deep Belief Networks 662 20.4 Deep Boltzmann Machines 665 20.5 Boltzmann Machines for real-Valued data .678 20.6 Convolutional boltzmann machines 20.7 Boltzmann Machines for Structured or Sequential Outputs .687 20.8 Other Boltzmann Machines 20.9 Back-Propagation through Random Operations 689 20.10 Directed Generative Nets 694 20 11 Drawing Samples from Autoencoders ..712 20.12 Generative Stochastic Networks 716 20.13 Other Generation schemes 717 20.14 Evaluating generative Models .719 20.15 Conclusion .721 Bibliography 723 Index 780 Website www.cleeplearlinlgboOk.org This book is accompanied by the above website. The website provides a variety of supplementary material, including exercises, lecture slides, corrections of mistakes, and other resources that should be useful to both readers and instructors Acknowledgments This book would not have been possible without the contributions of many people We would like to thank those who commented on our proposal for the book and helped plan its contents and organization: Guillaume Alain, Kyunghyun Cho Caglar gilcehre, David Krueger, Hugo larochelle, razvan Pascanu and Thomas Rohee We would like to thank the people who offered feedback on the content of the book itself. Some offered feedback on many chapters: Martin Abadi, Guillaume Alain, Ion Androutsopoulos, Fred Bertsch, Olexa Bilaniuk, Ufuk Can Bicici, Matko BoSnjak, John boersma, Greg brockman, Alexandre de brebisson, Pierre Luc Carrier, Sarath Chandar, Pawel Chilinski, Mark Daoust, Oleg Dashevskii, Laurent Dinh, Stephan Dreseitl, Jim Fan, Miao Fan, Meire Fortunato, Frederic francis Nando de Freitas, Caglar gulcehre, Jurgen Van Gael, Javier Alonso Garcia Jonathan Hunt, gopi Jeyaram, Chingiz Kabytayev, Lukasz Kaiser, Varun Kanade Akiel Khan John King, Diederik P. Kingina, Yanm Lecun, Rudolf mathey Matias Mattamala, Abhinav Maurya, Kevin Murphy, Oleg Murk, Roman Novak, Augustus Q. Odena, Simon Pavlik, Karl Pichotta, Kari Pulli, Roussel Rahman, Tapani Raiko Anurag ranjan, Johannes Roith, Mihaela rosca, Halis sak, Cesar Salgado, grigory Sapunov, Yoshinori Sasaki, Mike Schuster, Julian Serban, Nir Shabat, Ken Shirriff Andre Simpelo, Scott Stanley, David Sussillo, Ilya Sutskever, Carles Gelada saez Graham taylor, Valentin Tolmer, An Tran, Shubhendu Trivedi, Alexey umnov Vincent Vanhoucke, Marco Visentini-Scarzanella, David Warde-Farley, dustin Webb, Kelvin Xu, Wei Xue, Ke Yang, Li Yao, Zygmunt Zajac and Ozan Caglayan We would also like to thank those who provided us with useful feedback on individual chapters Notation: Zhang Yuanhang e Chapter 1, Introduction: Yusuf Akgul, Sebastien Bratieres, Samira Ebrahimi Charlie gorichanaz. Brendan loudermilk. Eric morris, Cosmin parvulescu CONTENTS and alfredo solano Chapter 2, Linear Algebra: Amjad Almahairi, Nikola banic, Kevin Bennett Philippe castonguay, Oscar Chang, Eric Fosler-Lussier, Andrey Khalyavin Sergey oreshkov, Istvan Petras. Dennis Prangle, Thomas rohee, Colby Toland. Massimiliano Tornassoli. Alessandro vitale and bob welland hapter 3, Probability and Information Theory: John Philip anderson, Kai Arulkumaran, Vincent Dumoulin, Rui Fa, Stephan Gouws, Artem Oboturov Antti Rasmus, Alexey Surkov and Volker Tresp e Chapter 4, Numerical Computation: Tran Lam An, Ian Fischer, and hu Yuhuang Chapter 5, Machine Learning Basics: Dzinitry Bahdanau, Nikhil G Tal Makoto Otsuka, Bob Pepin, Philip Popien, Emmanuel Rayner, Kee-Bong Song, Zheng Sun and Andy Wu Chapter 6, Deep Feedforward Networks: Uriel Berdugo, Fabrizio bottarel Elizabeth Burl, Ishan Durugkar, Jeff Hlywa, Jong Wook Kim, David Krueger and Aditya Kumar Praharaj Chapter 7, Regularization for Deep Learning: Kshitij Lauria, Inkyu Lee Sunil mohan and Joshua salisbury Chapter 8, Optimization for Training Deep Models: Marcel Ackermann Rowcl Atienza, Andrew Brock, Tegan Maharaj, James Martens, Klaus strobl and martin vita Chapter 9, Convolutional Networks: Martin Arjovsky, Eugene Brevdo, Kon- Pierce, Marjorie Sayer, Ryan Stout and Wentao Wy irza, Alex Paino, Eddie stantin diviloy Eric Jensen. Asifullah Khan Mehdi mirza Alex paino. edd Chapter 10, Sequence Modeling: Recurrent and Recursive Nets: Gokcen Eraslan, Steven Hickson, Razvan Pascanu, Lorenzo von Ritter, Rui rodrigues Dmitriy Scrdyuk, Dongyu Shi and Kaiyu Y Chapter 11, Practical Methodology: Daniel Beckstein e Chapter 12, Applications: George Dahl and Ribana roscher Chapter 15, Representation Learning: Kunal Ghosh IX

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