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Author:
Ian Goodfellow Yoshua Bengio Aaron Courville
Contents Website vii Acknowledgments viii Notation xi 1 Introduction 1 1.1 Who Should Read This Book? . . . . . . . . . . . . . . . . . . . . 8 1.2 Historical Trends in Deep Learning . . . . . . . . . . . . . . . . . 11 I Applied Math and Machine Learning Basics 29 2 Linear Algebra 31 2.1 Scalars, Vectors, Matrices and Tensors . . . . . . . . . . . . . . . 31 2.2 Multiplying Matrices and Vectors . . . . . . . . . . . . . . . . . . 34 2.3 Identity and Inverse Matrices . . . . . . . . . . . . . . . . . . . . 36 2.4 Linear Dependence and Span . . . . . . . . . . . . . . . . . . . . 37 2.5 Norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.6 Special Kinds of Matrices and Vectors . . . . . . . . . . . . . . . 40 2.7 Eigendecomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.8 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . 44 2.9 The Moore-Penrose Pseudoinverse . . . . . . . . . . . . . . . . . . 45 2.10 The Trace Operator . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.11 The Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.12 Example: Principal Components Analysis . . . . . . . . . . . . . 48 3 Probability and Information Theory 53
3.1 Why Probability? . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.2 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . 56 3.4 Marginal Probability . . . . . . . . . . . . . . . . . . . . . . . . . 58 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 . . . . . . . . . . . . . . . . . . . . . . . 80 4.2 Poor Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.3 Gradient-Based Optimization . . . . . . . . . . . . . . . . . . . . 82 4.4 Constrained Optimization . . . . . . . . . . . . . . . . . . . . . . 93 4.5 Example: Linear Least Squares . . . . . . . . . . . . . . . . . . . 96 5 Machine Learning Basics 98 5.1 Learning Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 Capacity, Overfitting and Underfitting . . . . . . . . . . . . . . . 110 5.3 Hyperparameters and Validation Sets . . . . . . . . . . . . . . . . 120 5.4 Estimators, Bias and Variance . . . . . . . . . . . . . . . . . . . . 122 5.5 Maximum Likelihood Estimation . . . . . . . . . . . . . . . . . . 131 5.6 Bayesian Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.7 Supervised Learning Algorithms . . . . . . . . . . . . . . . . . . . 139 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 6.3 Hidden Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 6.4 Architecture Design . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . 230 7.2 Norm Penalties as Constrained Optimization . . . . . . . . . . . . 237 7.3 Regularization and Under-Constrained Problems . . . . . . . . . 239 7.4 Dataset Augmentation . . . . . . . . . . . . . . . . . . . . . . . . 240 7.5 Noise Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 7.6 Semi-Supervised Learning . . . . . . . . . . . . . . . . . . . . . . 244 7.7 Multi-Task Learning . . . . . . . . . . . . . . . . . . . . . . . . . 245 7.8 Early Stopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 7.9 Parameter Tying and Parameter Sharing . . . . . . . . . . . . . . 251 7.10 Sparse Representations . . . . . . . . . . . . . . . . . . . . . . . . 253 7.11 Bagging and Other Ensemble Methods . . . . . . . . . . . . . . . 255 7.12 Dropout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 7.13 Adversarial Training . . . . . . . . . . . . . . . . . . . . . . . . . 267 7.14 Tangent Distance, Tangent Prop, and Manifold Tangent Classifier 268 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 8.4 Parameter Initialization Strategies . . . . . . . . . . . . . . . . . 301 8.5 Algorithms with Adaptive Learning Rates . . . . . . . . . . . . . 306 8.6 Approximate Second-Order Methods . . . . . . . . . . . . . . . . 310 8.7 Optimization Strategies and Meta-Algorithms . . . . . . . . . . . 318 9 Convolutional Networks 331 9.1 The Convolution Operation . . . . . . . . . . . . . . . . . . . . . 332 9.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 9.3 Pooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 9.4 Convolution and Pooling as an Infinitely Strong Prior . . . . . . . 346 9.5 Variants of the Basic Convolution Function . . . . . . . . . . . . 348 9.6 Structured Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . 359 9.7 Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 9.8 Efficient Convolution Algorithms . . . . . . . . . . . . . . . . . . 363
9.9 Random or Unsupervised Features . . . . . . . . . . . . . . . . . 364 9.10 The Neuroscientific Basis for Convolutional Networks . . . . . . . 365 9.11 Convolutional Networks and the History of Deep Learning . . . . 372 10 Sequence Modeling: Recurrent and Recursive Nets 374 10.1 Unfolding Computational Graphs . . . . . . . . . . . . . . . . . . 376 10.2 Recurrent Neural Networks . . . . . . . . . . . . . . . . . . . . . 379 10.3 Bidirectional RNNs . . . . . . . . . . . . . . . . . . . . . . . . . . 396 10.4 Encoder-Decoder Sequence-to-Sequence Architectures . . . . . . . 397 10.5 Deep Recurrent Networks . . . . . . . . . . . . . . . . . . . . . . 399 10.6 Recursive Neural Networks . . . . . . . . . . . . . . . . . . . . . . 401 10.7 The Challenge of Long-Term Dependencies . . . . . . . . . . . . . 403 10.8 Echo State Networks . . . . . . . . . . . . . . . . . . . . . . . . . 406 10.9 Leaky Units and Other Strategies for Multiple Time Scales . . . . 409 10.10 The Long Short-Term Memory and Other Gated RNNs . . . . . . 411 10.11 Optimization for Long-Term Dependencies . . . . . . . . . . . . . 415 10.12 Explicit Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 11 Practical methodology 424 11.1 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . 425 11.2 Default Baseline Models . . . . . . . . . . . . . . . . . . . . . . . 428 11.3 Determining Whether to Gather More Data . . . . . . . . . . . . 429 11.4 Selecting Hyperparameters . . . . . . . . . . . . . . . . . . . . . . 430 11.5 Debugging Strategies . . . . . . . . . . . . . . . . . . . . . . . . . 439 11.6 Example: Multi-Digit Number Recognition . . . . . . . . . . . . . 443 12 Applications 446 12.1 Large Scale Deep Learning . . . . . . . . . . . . . . . . . . . . . . 446 12.2 Computer Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 12.3 Speech Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . 461 12.4 Natural Language Processing . . . . . . . . . . . . . . . . . . . . 464 12.5 Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 480 III Deep Learning Research 489 13 Linear Factor Models 492 13.1 Probabilistic PCA and Factor Analysis . . . . . . . . . . . . . . . 493 13.2 Independent Component Analysis (ICA) . . . . . . . . . . . . . . 494
13.3 Slow Feature Analysis . . . . . . . . . . . . . . . . . . . . . . . . 496 13.5 Manifold Interpretation of PCA . . . . . . . . . . . . . . . . . . . 502 14 Autoencoders 505 14.1 Undercomplete Autoencoders . . . . . . . . . . . . . . . . . . . . 506 14.2 Regularized Autoencoders . . . . . . . . . . . . . . . . . . . . . . 507 14.3 Representational Power, Layer Size and Depth . . . . . . . . . . . 511 14.4 Stochastic Encoders and Decoders . . . . . . . . . . . . . . . . . . 512 14.5 Denoising Autoencoders . . . . . . . . . . . . . . . . . . . . . . . 513 14.6 Learning Manifolds with Autoencoders . . . . . . . . . . . . . . . 518 14.7 Contractive Autoencoders . . . . . . . . . . . . . . . . . . . . . . 524 14.8 Predictive Sparse Decomposition . . . . . . . . . . . . . . . . . . 526 14.9 Applications of Autoencoders . . . . . . . . . . . . . . . . . . . . 527 15 Representation Learning 529 15.1 Greedy Layer-Wise Unsupervised Pretraining . . . . . . . . . . . 531 15.2 Transfer Learning and Domain Adaptation . . . . . . . . . . . . . 539 15.3 Semi-Supervised Disentangling of Causal Factors . . . . . . . . . 544 15.4 Distributed Representation . . . . . . . . . . . . . . . . . . . . . . 549 15.5 Exponential Gains from Depth . . . . . . . . . . . . . . . . . . . 556 15.6 Providing Clues to Discover Underlying Causes . . . . . . . . . . 557 16 Structured Probabilistic Models for Deep Learning 561 16.1 The Challenge of Unstructured Modeling . . . . . . . . . . . . . . 562 16.2 Using Graphs to Describe Model Structure . . . . . . . . . . . . . 566 16.3 Sampling from Graphical Models . . . . . . . . . . . . . . . . . . 583 16.4 Advantages of Structured Modeling . . . . . . . . . . . . . . . . . 584 16.5 Learning about Dependencies . . . . . . . . . . . . . . . . . . . . 585 16.6 Inference and Approximate Inference . . . . . . . . . . . . . . . . 586 16.7 The Deep Learning Approach to Structured Probabilistic Models 587 17 Monte Carlo Methods 593 17.1 Sampling and Monte Carlo Methods . . . . . . . . . . . . . . . . 593 17.2 Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . 595 17.3 Markov Chain Monte Carlo Methods . . . . . . . . . . . . . . . . 598 17.4 Gibbs Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602 17.5 The Challenge of Mixing between Separated Modes . . . . . . . . 602 18 Confronting the Partition Function 608 18.1 The Log-Likelihood Gradient . . . . . . . . . . . . . . . . . . . . 609
18.2 Stochastic Maximum Likelihood and Contrastive Divergence . . . 610 18.3 Pseudolikelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . 618 18.4 Score Matching and Ratio Matching . . . . . . . . . . . . . . . . 620 18.5 Denoising Score Matching . . . . . . . . . . . . . . . . . . . . . . 622 18.6 Noise-Contrastive Estimation . . . . . . . . . . . . . . . . . . . . 623 18.7 Estimating the Partition Function . . . . . . . . . . . . . . . . . . 626 19 Approximate inference 634 19.1 Inference as Optimization . . . . . . . . . . . . . . . . . . . . . . 636 19.2 Expectation Maximization . . . . . . . . . . . . . . . . . . . . . . 637 19.3 MAP Inference and Sparse Coding . . . . . . . . . . . . . . . . . 638 19.4 Variational Inference and Learning . . . . . . . . . . . . . . . . . 641 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 . . . . . . . . . . . . . . . . . 685 20.7 Boltzmann Machines for Structured or Sequential Outputs . . . . 687 20.8 Other Boltzmann Machines . . . . . . . . . . . . . . . . . . . . . 688 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 | 
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发表于 2016-4-9 09:01:04
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