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概率视角下的机器学习:原理与应用
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更新于2024-07-19
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《机器学习:概率视角》是一本由Kevin P. Murphy撰写的权威教材,专为现代网络环境下对大规模电子数据进行自动化分析的需求而设计。该书系统地介绍了机器学习领域,强调了概率方法在其中的核心作用。它提供了一个全面且自成体系的入门教程,将深度与广度结合,涵盖了必要的基础知识,如概率论、优化和线性代数,同时紧跟最新进展,讨论了条件随机场、L1正则化以及深度学习等前沿技术。 作者以通俗易懂的风格书写,辅以重要的算法伪代码,使得复杂概念易于理解。书中大量使用彩色图像和实际应用示例,如生物学、文本处理、计算机视觉和机器人学等领域,帮助读者更好地将理论与实践相结合。作者倡导基于模型的系统性方法,常以图形模型的语言简洁而直观地表述模型,这种策略使得学习过程更具连贯性和洞察力。 值得一提的是,书中大部分讨论的模型都有一个名为PMTK(概率建模工具包)的MATLAB软件包支持,该工具包是免费提供的,方便读者在实践中应用所学知识。这本书的目标读者群包括具有初级大学数学背景的高年级本科生和初入门的研究生,旨在培养他们理解和掌握机器学习的基本原理和实践技巧。 《机器学习:概率视角》不仅涵盖了扎实的理论基础,而且注重实际应用,是一本对于希望在这个快速发展的领域深入探索的学生和专业人士来说不可或缺的参考书。通过学习本书,读者不仅能掌握机器学习的基础,还能培养出从概率的角度去理解和解决实际问题的能力。
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![](https://csdnimg.cn/release/download_crawler_static/10292785/bg10.jpg)
CONTENTS xv
13.4.2 LARS and other homotopy methods 441
13.4.3 Proximal and gradient projection methods 442
13.4.4 EM for lasso 447
13.5
1
regularization: extensions 449
13.5.1 Group Lasso 449
13.5.2 Fused lasso 454
13.5.3 Elastic net (ridge and lasso combined) 455
13.6 Non-convex regularizers 457
13.6.1 Bridge regression 458
13.6.2 Hierarchical adaptive lasso 458
13.6.3 Other hierarchical priors 462
13.7 Automatic relevance determination (ARD)/sparse Bayesian learning (SBL) 463
13.7.1 ARD for linear regression 463
13.7.2 Whence sparsity? 465
13.7.3 Connection to MAP estimation 465
13.7.4 Algorithms for ARD * 466
13.7.5 ARD for logistic regression 468
13.8 Sparse coding * 468
13.8.1 Learning a sparse coding dictionary 469
13.8.2 Results of dictionary learning from image patches 470
13.8.3 Compressed sensing 472
13.8.4 Image inpainting and denoising 472
14 Kernels 479
14.1 Introduction 479
14.2 Kernel functions 479
14.2.1 RBF kernels 480
14.2.2 Kernels for comparing documents 480
14.2.3 Mercer (positive definite) kernels 481
14.2.4 Linear kernels 482
14.2.5 Matern kernels 482
14.2.6 String kernels 483
14.2.7 Pyramid match kernels 484
14.2.8 Kernels derived from probabilistic generative models 485
14.3 Using kernels inside GLMs 486
14.3.1 Kernel machines 486
14.3.2 L1VMs, RVMs, and other sparse vector machines 487
14.4 The kernel trick 488
14.4.1 Kernelized nearest neighbor classification 489
14.4.2 Kernelized K-medoids clustering 489
14.4.3 Kernelized ridge regression 492
14.4.4 Kernel PCA 493
14.5 Support vector machines (SVMs) 496
14.5.1 SVMs for regression 497
14.5.2 SVMs for classification 498
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xvi CONTENTS
14.5.3 Choosing C 504
14.5.4 Summary of key points 504
14.5.5 A probabilistic interpretation of SVMs 505
14.6 Comparison of discriminative kernel methods 505
14.7 Kernels for building generative models 507
14.7.1 Smoothing kernels 507
14.7.2 Kernel density estimation (KDE) 508
14.7.3 From KDE to KNN 509
14.7.4 Kernel regression 510
14.7.5 Locally weighted regression 512
15 Gaussian processes 515
15.1 Introduction 515
15.2 GPs for regression 516
15.2.1 Predictions using noise-free observations 517
15.2.2 Predictions using noisy observations 518
15.2.3 Eect of the kernel parameters 519
15.2.4 Estimating the kernel parameters 521
15.2.5 Computational and numerical issues * 524
15.2.6 Semi-parametric GPs * 524
15.3 GPs meet GLMs 525
15.3.1 Binary classification 525
15.3.2 Multi-class classification 528
15.3.3 GPs for Poisson regression 531
15.4 Connection with other methods 532
15.4.1 Linear models compared to GPs 532
15.4.2 Linear smoothers compared to GPs 533
15.4.3 SVMs compared to GPs 534
15.4.4 L1VM and RVMs compared to GPs 534
15.4.5 Neural networks compared to GPs 535
15.4.6 Smoothing splines compared to GPs * 536
15.4.7 RKHS methods compared to GPs * 538
15.5 GP latent variable model 540
15.6 Approximation methods for large datasets 542
16 Adaptive basis function models 543
16.1 Introduction 543
16.2 Classification and regression trees (CART) 544
16.2.1 Basics 544
16.2.2 Growing a tree 545
16.2.3 Pruning a tree 549
16.2.4 Pros and cons of trees 550
16.2.5 Random forests 550
16.2.6 CART compared to hierarchical mixture of experts * 551
16.3 Generalized additive models 552
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CONTENTS xvii
16.3.1 Backfitting 552
16.3.2 Computational eciency 553
16.3.3 Multivariate adaptive regression splines (MARS) 553
16.4 Boosting 554
16.4.1 Forward stagewise additive modeling 555
16.4.2 L2boosting 557
16.4.3 AdaBoost 558
16.4.4 LogitBoost 559
16.4.5 Boosting as functional gradient descent 560
16.4.6 Sparse boosting 561
16.4.7 Multivariate adaptive regression trees (MART) 562
16.4.8 Why does boosting work so well? 562
16.4.9 A Bayesian view 563
16.5 Feedforward neural networks (multilayer perceptrons) 563
16.5.1 Convolutional neural networks 564
16.5.2 Other kinds of neural networks 568
16.5.3 A brief history of the field 568
16.5.4 The backpropagation algorithm 569
16.5.5 Identifiability 572
16.5.6 Regularization 572
16.5.7 Bayesian inference * 576
16.6 Ensemble learning 580
16.6.1 Stacking 580
16.6.2 Error-correcting output codes 581
16.6.3 Ensemble learning is not equivalent to Bayes model averaging 581
16.7 Experimental comparison 582
16.7.1 Low-dimensional features 582
16.7.2 High-dimensional features 583
16.8 Interpreting black-box models 585
17 Markov and hidden Markov models 589
17.1 Introduction 589
17.2 Markov models 589
17.2.1 Transition matrix 589
17.2.2 Application: Language modeling 591
17.2.3 Stationary distribution of a Markov chain * 596
17.2.4 Application: Google’s PageRank algorithm for web page ranking * 600
17.3 Hidden Markov models 603
17.3.1 Applications of HMMs 604
17.4 Inference in HMMs 606
17.4.1 Types of inference problems for temporal models 606
17.4.2 The forwards algorithm 609
17.4.3 The forwards-backwards algorithm 610
17.4.4 The Viterbi algorithm 612
17.4.5 Forwards filtering, backwards sampling 616
![](https://csdnimg.cn/release/download_crawler_static/10292785/bg13.jpg)
xviii CONTENTS
17.5 Learning for HMMs 617
17.5.1 Training with fully observed data 617
17.5.2 EM for HMMs (the Baum-Welch algorithm) 618
17.5.3 Bayesian methods for “fitting” HMMs * 620
17.5.4 Discriminative training 620
17.5.5 Model selection 621
17.6 Generalizations of HMMs 621
17.6.1 Variable duration (semi-Markov) HMMs 622
17.6.2 Hierarchical HMMs 624
17.6.3 Input-output HMMs 625
17.6.4 Auto-regressive and buried HMMs 626
17.6.5 Factorial HMM 627
17.6.6 Coupled HMM and the influence model 628
17.6.7 Dynamic Bayesian networks (DBNs) 628
18 State space models 631
18.1 Introduction 631
18.2 Applications of SSMs 632
18.2.1 SSMs for object tracking 632
18.2.2 Robotic SLAM 633
18.2.3 Online parameter learning using recursive least squares 636
18.2.4 SSM for time series forecasting * 637
18.3 Inference in LG-SSM 640
18.3.1 The Kalman filtering algorithm 640
18.3.2 The Kalman smoothing algorithm 643
18.4 Learning for LG-SSM 646
18.4.1 Identifiability and numerical stability 646
18.4.2 Training with fully observed data 647
18.4.3 EM for LG-SSM 647
18.4.4 Subspace methods 647
18.4.5 Bayesian methods for “fitting” LG-SSMs 647
18.5 Approximate online inference for non-linear, non-Gaussian SSMs 647
18.5.1 Extended Kalman filter (EKF) 648
18.5.2 Unscented Kalman filter (UKF) 650
18.5.3 Assumed density filtering (ADF) 652
18.6 Hybrid discrete/continuous SSMs 655
18.6.1 Inference 656
18.6.2 Application: data association and multi-target tracking 658
18.6.3 Application: fault diagnosis 659
18.6.4 Application: econometric forecasting 660
19 Undirected graphical models (Markov random fields) 661
19.1 Introduction 661
19.2 Conditional independence properties of UGMs 661
19.2.1 Key properties 661
![](https://csdnimg.cn/release/download_crawler_static/10292785/bg14.jpg)
CONTENTS xix
19.2.2 An undirected alternative to d-separation 663
19.2.3 Comparing directed and undirected graphical models 664
19.3 Parameterization of MRFs 665
19.3.1 The Hammersley-Cliord theorem 665
19.3.2 Representing potential functions 667
19.4 Examples of MRFs 668
19.4.1 Ising model 668
19.4.2 Hopfield networks 669
19.4.3 Potts model 671
19.4.4 Gaussian MRFs 672
19.4.5 Markov logic networks * 674
19.5 Learning 676
19.5.1 Training maxent models using gradient methods 676
19.5.2 Training partially observed maxent models 677
19.5.3 Approximate methods for computing the MLEs of MRFs 678
19.5.4 Pseudo likelihood 678
19.5.5 Stochastic maximum likelihood 679
19.5.6 Feature induction for maxent models * 680
19.5.7 Iterative proportional fitting (IPF) * 681
19.6 Conditional random fields (CRFs) 684
19.6.1 Chain-structured CRFs, MEMMs and the label-bias problem 684
19.6.2 Applications of CRFs 686
19.6.3 CRF training 692
19.7 Structural SVMs 693
19.7.1 SSVMs: a probabilistic view 693
19.7.2 SSVMs: a non-probabilistic view 695
19.7.3 Cutting plane methods for fitting SSVMs 698
19.7.4 Online algorithms for fitting SSVMs 700
19.7.5 Latent structural SVMs 701
20 Exact inference for graphical models 707
20.1 Introduction 707
20.2 Belief propagation for trees 707
20.2.1 Serial protocol 707
20.2.2 Parallel protocol 709
20.2.3 Gaussian BP * 710
20.2.4 Other BP variants * 712
20.3 The variable elimination algorithm 714
20.3.1 The generalized distributive law * 717
20.3.2 Computational complexity of VE 717
20.3.3 A weakness of VE 720
20.4 The junction tree algorithm * 720
20.4.1 Creating a junction tree 720
20.4.2 Message passing on a junction tree 722
20.4.3 Computational complexity of JTA 725
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