Machine learning: a probabilistic perspective
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, Massachusetts ; London, England
The MIT Press
[2012]
|
| Schriftenreihe: | Adaptive computation and machine learning series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xxix, 1071 Seiten Illustrationen, Diagramme |
| ISBN: | 9780262018029 9780262305242 |
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| 100 | 1 | |a Murphy, Kevin P. |d 1970- |0 (DE-588)1026956137 |4 aut | |
| 245 | 1 | 0 | |a Machine learning |b a probabilistic perspective |c Kevin P. Murphy |
| 264 | 1 | |a Cambridge, Massachusetts ; London, England |b The MIT Press |c [2012] | |
| 264 | 4 | |c © 2012 | |
| 300 | |a xxix, 1071 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Adaptive computation and machine learning series | |
| 500 | |a Includes bibliographical references and index | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Machine learning | |
| 650 | 4 | |a Probabilities | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Maschinelles Lernen |0 (DE-588)4193754-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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| 689 | 0 | 1 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |D s |
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Datensatz im Suchindex
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| _version_ | 1816842961372053504 |
| adam_text | Contents
Preface
xxvii
1
Introduction
1
LI
Machine
learning: what and why?
1
1.1.1
Types of machine learning
2
1.2
Supervised learning
3
1.2.1
Classification
3
1.2.2
Regression
8
1.3
Unsupervised learning
9
1.3.1
Discovering clusters
10
1.3.2
Discovering latent factors
11
1.3.3
Discovering graph structure
13
1.3.4
Matrix completion
14
1.4
Some basic concepts in machine learning
16
1.4.1
Parametric vs non-parametric models
16
1.4.2
A simple non-parametric classifier: i-i-nearest neighbors
16
1.4.3
The curse of dimensionality
18
1.4.4
Parametric models for classification and regression
19
1.4.5
Linear regression
19
1.4.6
Logistic regression
21
1.4.7
Overfitting
22
1.4.8
Model selection
22
1.4.9
No free lunch theorem
24
2
Probability
27
2.1
Introduction
27
2.2
A brief review of probability theory
28
2.2.1
Discrete random variables
28
2.2.2
Fundamental rules
28
2.2.3
Bayes
rale
29
2.2.4
Independence and conditional independence
30
2.2.5
Continuous random variables
32
viii CONTENTS
2.2.6
Quantités
33
2.2.7
Mean and variance
33
2.3
Some common discrete distributions
34
2.3.1
The binomial and Bernoulli distributions
34
2.3.2
The multinomial and multinouffi distributions
35
2.3.3
The
Poisson
distribution
37
2.3.4
The empirical distribution
37
2.4
Some common continuous distributions
38
2.4.1
Gaussian (normal) distribution
38
2.4.2
Degenerate
pdf 39
2.4.3
The Laplace distribution
41
2.4.4
The gamma distribution
41
2.4.5
The beta distribution
42
2.4.6
Pareto distribution
43
2.5
Joint probability distributions
44
2.5.1
Covariance and correlation
44
2.5.2
The multivariate Gaussian
46
2.5.3
Multivariate Student
t
distribution
46
2.5.4
Dirichlet distribution
47
2.6
Transformations of random variables
49
2.6.1
Linear transformations
49
2.6.2
General transformations
50
2.6.3
Central limit theorem
51
2.7
Monte
Cario
approximation
52
2.7.1
Example: change of variables, the
MC
way
53
2.7.2
Example: estimating
тг
by Monte Carlo integration
54
2.7.3
Accuracy of Monte Carlo approximation
54
2.8
Information theory
56
2.8.1
Entropy
56
2.8.2
KL divergence
57
2.8.3
Mutual information
59
3
Generative models for discrete data
65
3.1
Introduction
65
3.2
Bayesian concept learning
65
3.2.1
Likelihood
67
3.2.2
Prior
67
3.2.3
Posterior
68
3.2.4
Posterior predictive distribution
71
3.2.5
A more complex prior
72
3.3
The beta-binomial model
72
3.3.1
Likelihood
73
3.3.2
Prior
74
3.3.3
Posterior
75
3.3.4
Posterior predictive distribution
77
CONTENTS ix
3.4 The
Dirichlet-multmomiał model
78
3.4.1
Likelihood
79
3.4.2
Prior
79
3.4.3
Posterior
79
3.4.4
Posterior predictive
81
3.5
Naive
Bayes
classifiers
82
3.5.1
Model fitting
83
3.5.2
Using the model for prediction
85
3.5.3
The log-sum-exp trick
86
3.5.4
Feature selection using mutual information
86
3.5.5
Classifying documents using bag of words
87
4
Gaussian models
97
4.1
Introduction
97
4.1.1
Notation
97
4.L2 Basics
97
4.1.3
MLE for an MVN
99
4.1.4
Maximum entropy derivation of the Gaussian
* 101
4.2
Gaussian discriminant analysis
101
4.2.1
Quadratic discriminant analysis (QDA)
102
4.2.2
Linear discriminant analysis (LDA)
103
4.2.3
Two-class LDA
104
4.2.4
MLE for discriminant analysis
106
4.2.5
Strategies for preventing overfitting
106
4.2.6
Regularized LDA
* 107
4.2.7
Diagonal LDA
108
4.2.8
Nearest shrunken
centroide
classifier
* 109
4.3
Inference in jointly Gaussian distributions
110
4.3.1
Statement of the result 111
4.3.2
Examples
Ш
4.3.3
Information form
115
4.3.4
Proof of the result
* 116
4.4
Linear Gaussian systems
119
4.4.1
Statement of the result
119
4.4.2
Examples
120
4.4.3
Proof of the result
* 124
4.5
Digression: The
Wishart
distribution
* 125
4.5.1
Inverse
Wishart
distribution
126
4.5.2
Visualizing the
Wishart
distribution
* 127
4.6
Inferring the parameters of an MVN
127
4.6.1
Posterior distribution of
μ
128
4.6.2
Posterior distribution of
Σ
* 128
4.6.3
Posterior distribution of
μ
and
Σ
* 132
4.6.4
Sensor fusion with unknown precisions
* 138
CONTENTS
5 Bayesian
statistics
149
5.1
Introduction
149
5.2
Summarizing posterior distributions
149
5.2.1
MAP estimation
149
5.2.2
Credible intervals
152
5.2.3
Inference for a difference in proportions
154
5.3
Bayesian model selection
155
5.3.1
Bayesian Occam s razor
156
5.3.2
Computing the marginal likelihood (evidence)
158
5.3.3
Bayes
factors
163
5.3.4
Jeffreys-Lindley paradox
* 164
5.4
Priors
165
5.4.1
Uninformative priors
165
5.4.2
Jeffreys priors
* 166
5.4.3
Robust priors
168
5.4.4
Mixtures of conjugate priors
168
5.5
Hierarchical
Bayes
171
5.5.1
Example: modeling related cancer rates
171
5.6
Empirical
Bayes
172
5.6.1
Example: beta-binomial model
173
5.6.2
Example: Gaussian-Gaussian model
173
5.7
Bayesian decision theory
176
5.7.1
Bayes
estimators for common loss functions
177
5.7.2
The false positive vs false negative tradeoff
180
5.7.3
Other
topics
* 184
6
Frequentisi
statistics
191
6.1
Introduction
191
6.2
Sampling distribution of an estimator
191
6.2.1
Bootstrap
192
6.2.2
Large sample theory for the MLE
* 193
6.3
Frequentisi
decision theory
194
6.3.1
Bayes
risk
195
6.3.2
Minimax risk
196
6.3.3
Admissible estimators
197
6.4
Desirable properties of estimators
200
6.4.1
Consistent estimators
200
6.4.2
Unbiased estimators
200
6.4.3
Minimum variance estimators
201
6.4.4
The bias-variance tradeoff
202
6.5
Empirical risk minimisation
204
6.5.1
Regularized risk minimization
205
6.5.2
Structural risk minimization
206
6.5.3
Estimating the risk using cross validation
206
6.5.4
Upper bounding the risk using statistical learning theory
* 209
CONTENTS xi
6.5.5 Surrogate
loss functions
210
6.6
Pathologies of
frequentisi
statistics
* 211
6.6.1
Counter-intuitive behavior of confidence intervals
212
6.6.2
p-values considered harmful
213
6.6.3
The likelihood principle
214
6.6.4
Why isn t everyone a Bayesian?
215
7
Linear regression
217
7.1
Introduction
217
7.2
Model specification
217
7.3
Maximum likelihood estimation (least squares)
217
7.3.1
Derivation of the MLE
219
7.3.2
Geometric interpretation
220
7.3.3
Convexity
221
7.4
Robust linear regression
* 223
7.5
Ridge regression
225
7.5.1
Basic idea
225
7.5.2
Numerically stable computation
* 227
7.5.3
Connection with PCA
* 228
7.5.4
Regularization effects of big data
230
7.6
Bayesian linear regression
231
7.6.1
Computing the posterior
232
7.6.2
Computing the posterior predictive
233
7.6.3
Bayesian inference when
σ2
is unknown
* 234
7.6.4
EB for linear regression (evidence procedure)
238
8
Logistic regression
245
8.1
Introduction
245
8.2
Model specification
245
8.3
Model fitting
245
8.3.1
MLE
246
8.3.2
Steepest descent
247
8.3.3
Newton s method
249
8.3.4
Iteratively reweighted least squares (fflLS)
250
8.3.5
Quasi-Newton
(variable metric) methods
251
8.3.6
£2 regularization
252
8.3.7
Multi-class logistic regression
252
8.4
Bayesian logistic regression
254
8.4.1
Laplace approximation
255
8.4.2
Derivation of the
BIC
255
8.4.3
Gaussian approximation for logistic regression
256
8.4.4
Approximating the posterior predictive
256
8.4.5
Residual analysis (outlier detection)
* 260
8.5
Online learning and stochastic optimization
261
8.5.1
Online learning and regret minimization
262
CONTENTS
8.5.2
Stochastic optimization and risk minimization
262
8.5.3
The LMS algorithm
264
8.5.4
The perceptron algorithm
265
8.5.5
A Bayesian view
266
8.6
Generative vs discriminative classifiers
267
8.6.1
Pros and cons of each approach
268
8.6.2
Dealing with missing data
269
8.6.3
Fisher s linear discriminant analysis (FLDA)
* 271
9
Generalized linear models and the exponential family
281
9.1
Introduction
281
9.2
The exponential family
281
9.2.1
Definition
282
9.2.2
Examples
282
9.2.3
Log partition function
284
9.2.4
MLE for the exponential family
286
9.2.5
Bayes
for the exponential family
* 287
9.2.6
Maximum entropy derivation of the exponential family
* 289
9.3
Generalized linear models (GLMs)
290
9.3.Í
Basics
290
9.3.2
ML and MAP estimation
292
9.3.3
Bayesian inference
293
9.4
Probit
regression
293
9.4.1
ML/MAP estimation using gradient-based optimization
294
9.4.2
Latent variable interpretation
294
9.4.3
Ordinai
probit
regression
* 295
9.4.4
Multinomial
probit
models
* 295
9.5
Multi-task learning
296
9.5.1
Hierarchical
Bayes
for multi-task learning
296
9.5.2
Application to personalized email spam filtering
296
9.5.3
Application to domain adaptation
297
9.5.4
Other kinds of prior
297
9.8
Generalized linear mixed models
* 298
9.6.1
Example: semi-parametric GLMMs for medical data
298
9.6.2
Computational issues
300
9.7
Learning to rank
* 300
9.7.1
The pointwise approach
301
9.7.2
The pairwise approach
301
9.7.3
The listwise approach
302
9.7.4
Loss functions for
ranking
303
10
Directed graphical models
(Bayes
nets)
30?
10.1
Introduction
307
10.1.1
Chain rule
307
10.1.2
Conditional independence
308
CONTENTS xiii
10.1.3
Graphical models
308
10.1.4
Graph terminology
309
10.1.5
Directed graphical models
310
10.2
Examples
311
10.2.1
Naive
Bayes
classifiers
311
10.2.2
Markov and hidden Markov models
312
10.2.3
Medical diagnosis
313
10.2.4
Genetic linkage analysis
* 315
10.2.5
Directed Gaussian graphical models
* 318
10.3
Inference
319
10.4
Learning
320
10.4.1
Plate notation
320
10.4.2
Learning from complete data
322
10.4.3
Learning with missing and/or latent variables
323
10.5
Conditional independence properties of DGMs
324
10.5.1
d-separation and the
Bayes
Ball algorithm (global Markov
properties)
324
10.5.2
Other Markov properties of DGMs
327
10.5.3
Markov blanket and full conditionals
327
10.6
Influence (decision) diagrams
* 328
11
Mixture models and the EM algorithm
337
11.1
Latent variable models
337
11.2
Mixture models
337
11.2.1
Mixtures of Gaussians
339
11.2.2
Mixture of multinouliis
340
11.2.3
Using mixture models for clustering
340
11.2.4
Mixtures of experts
342
11.3
Parameter estimation for mixture models
345
11.3.1
Unidentifiability
346
11.3.2
Computing a MAP estimate is non-convex
347
11.4
The EM algorithm
348
11.4.1
Basic idea
349
11.4.2
EM for GMMs
350
11.4.3
EM for mixture of experts
357
11.4.4
EM for DGMs with hidden variables
358
11.4.5
EM for the Student distribution
* 359
11.4.6
EM for
probit
regression
* 362
11.4.7
Theoretical basis for EM
* 363
11.4.8
Online EM
365
1L4.9 Other EM variants
* 367
11.5
Model selection for latent variable models
370
11.5.1
Model selection for probabilistic models
370
11.5.2
Model selection for non-probabilistic methods
370
11.6
Fitting models with missing data
372
CONTENTS
xiv
11.6.1 EM
for the
MLE
of an MVN with missing data
373
12
Latent linear models
381
12.1
Factor analysis
381
12.1.1
FA is a low rank parameterization of an MVN
381
12.1.2
Inference of the latent factors
382
12.1.3
Unidentifiability
383
12.1.4
Mixtures of factor analysers
385
12.1.5
EM for factor analysis models
386
12.1.6
Fitting FA models with missing data
387
12.2
Principal components analysis (PCA)
387
12.2.1
Classical PCA: statement of the theorem
387
12.2.2
Proof
* 389
12.2.3
Singular value decomposition
(SVD)
392
12.2.4
Probabilistic PCA
395
12.2.5
EM algorithm for PCA
396
12.3
Choosing the number of latent dimensions
398
12.3.1
Model selection for FA/PPCA
398
12.3.2
Model selection for PCA
399
12.4
PCA for categorical data
402
12.5
PCA for paired and multi-view data
404
12.5.1
Supervised PCA (latent factor regression)
405
12.5.2
Partial least squares
406
12.5.3
Canonical correlation analysis
407
12.6
Independent Component Analysis
(ICA)
407
12.6.1
Maximum likelihood estimation
410
12.6.2
The FastICA algorithm
411
12.6.3
Using EM
414
12.6.4
Other estimation principles
* 415
13
Sparse linear models
421
13.1
Introduction
421
13.2
Bayesian variable selection
422
13.2.1
The spike and slab model
424
13.2.2
From the Bernoulli-Gaussian model to £0 regularization
425
13.2.3
Algorithms
426
13.3
i¡
regularization: basics
429
13.3.1
Why does t regularization yield sparse solutions?
430
13.3.2
Optimality conditions for lasso
431
13.3.3
Comparison of least squares, lasso, ridge and subset selection
435
13.3.4
Regularization path
436
13.3.5
Model selection
439
13.3.6
Bayesian inference for linear models with Laplace priors
440
13.4
( ι
regularization: algorithms
441
13.4.1
Coordinate descent
441
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
¿Ί
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
LIVMs, 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
Kemelized 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
xvj
CONTENTS
14.5.3
Choosing
С
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
Effect 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-ciass 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
Ш
Adaptive basis function models
543
16.1
Introduction
543
Î6.2
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
CAM compared to hierarchical mixture of experts
* 551
16.3
Generalized additive models
552
CONTENTS xvii
16.3.1 Backfitting 552
16.3.2
Computational efficiency
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 Yiterbi algorithm
612
17.4.5
Forwards filtering, backwards sampling
616
coimNTS
XVUl
17.5
Learning for HMMs
617
17.5.1
Training with fully observed data
617
17.5.2
EM for HMMs (the Baum-Wekh 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
IS 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
Identiiability 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
Ш
Undirected graphical models (Markov random fields)
661
13.1
introduction
661
19.2
Condiţional
independence properties of UGMs
861
19,2.1
Key properties
661
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-Clifford 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
CONTENTS
xx
20.4.4 JTA
generalizations *
726
20.5
Computational intractability of exact inference in the worst case
726
9П Ч
1
Annrrodmatf» inference
727
21
Varlational inference
731
21.1
Introduction
731
21.2
Variational inference
732
21.2.1
Alternative interpretations of the variational objective
733
21.2.2
Forward or reverse KL?
* 733
21.3
The mean field method
735
21.3.1
Derivation of the mean field update equations
736
21.3.2
Example: mean field for the Ising model
737
21.4
Structured mean field
* 739
21.4.1
Example: factorial
HMM
740
21.5
Variational
Bayes
742
21.5.1
Example: VB for a univariate Gaussian
742
21.5.2
Example: VB for linear regression
746
21.6
Variational
Bayes
EM
749
21.6.1
Example: VBEM for mixtures of
Gaussiane
* 750
21.7
Variational message passing and VIBES
756
21.8
Local variational bounds
* 756
218.1
Motivating applications
756
21.8.2
Bohning s quadratic bound to the log-sum-exp function
758
21.8.3
Bounds for the sigmoid function
760
21.8.4
Other bounds and approximations to the log-sum-exp function
* 762
21.8.5
Variational inference based on upper bounds
763
22
More vuriutional inference
767
22.1
introduction
767
22.2
Loopy belief propagation: algorithmic issues
767
22.2.1
A brief history
767
22.2.2
LBP on pairwise models
768
22.2.3
LBP on a factor graph
769
22.2.4
Convergence
771
22.2.5
Accuracy of LBP
774
22.2.6
Other speedup tricks for LBP
* 775
22.3
Loopy belief propagation: theoretical issues
* 776
22.3.1
UGMs represented in exponential family form
776
22.3.2
The marginal polytope
777
22.3.3
Exact inference as a variational optimization problem
778
22J.4 Mean field as a variational optimization problem
779
22.3.5
LBP as a variational optimization problem
779
22.3.6
Loopy BP vs mean field
783
22.4
Extensions of belief propagation
* 783
22.4.1
Generalized belief propagation
783
CONTENTS xxi
22.4.2
Convex
belief propagation
785
22.5
Expectation propagation
787
22.5.1
EP as a variational inference problem
788
22.5.2
Optimizing the EP objective using moment matching
789
22.5.3
EP for the clutter problem
791
22.5.4
LBP is a special case of EP
792
22.5.5
Ranking players using TrueSkill
793
22.5.6
Other applications of EP
799
22.6
MAP state estimation
799
22.6.1
Linear programming relaxation
799
22.6.2
Max-product belief propagation
800
22.6.3
Graphcuts
801
22.6.4
Experimental comparison of graphcuts and BP
804
22.6.5
Dual decomposition
806
23
Monte Carlo inference
815
23.1
Introduction
815
23.2
Sampling from standard distributions
815
23.2.1
Using the cdf
815
23.2.2
Sampling from a Gaussian (Box-Muller method)
817
23.3
Rejection sampling
817
23.3.1
Basic idea
817
23.3.2
Example
818
23.3.3
Application to Bayesian statistics
819
23.3.4
Adaptive rejection sampling
819
23.3.5
Rejection sampling in high dimensions
820
23.4
Importance sampling
820
23.4.1
Basic idea
820
23.4.2
Handling urmormalized distributions
821
23.4.3
Importance sampling for a DGM: likelihood weighting
822
23.4.4
Sampling importance resampling (SIR)
822
23.5
Particle filtering
823
23.5.1
Sequential importance sampling
824
23.5.2
The degeneracy problem
825
23.5.3
The resampling step
825
23.5.4
The proposal distribution
827
23.5.5
Application: robot localization
828
23.5.6
Application: visual object tracking
828
23.5.7
Application: time series forecasting
831
23.6
Rao-Blackwellised particle filtering (RBPF)
831
23.6.1
RBPF for switching LG-SSMs
831
23.6.2
Application: tracking a maneuvering target
832
23.6.3
Application: Fast SLAM
834
24
Markov chain Monte Carlo (MCMC) inference
837
xxii
C0NTENTS
24.1
Introduction
837
24.2
Gibbs sampling
838
24.2.1
Basic
idea
838
24.2.2
Example: Gibbs sampling for the Ising model
838
24.2.3
Example: Gibbs sampling for inferring the parameters of a GMM
840
24.2.4
Collapsed Gibbs sampling
* 841
24.2.5
Gibbs sampling for hierarchical GLMs
844
24.2.6
BUGS and JAGS
846
24.2.7
The Imputation Posterior (IP) algorithm
847
24.2.8
Blocking Gibbs sampling
847
24.3
Metropolis Hastings algorithm
848
24.3.1
Basic idea
848
24.3.2
Gibbs sampling is a special case of MH
849
24.3.3
Proposal distributions
850
24.3.4
Adaptive MCMC
853
24.3.5
Initialization and mode hopping
854
24.3.6
Why MH works
* 854
24.3.7
Reversible jump (trans-dimensional) MCMC
* 855
24.4
Speed and accuracy of MCMC
856
24.4.1
The burn-in phase
856
24.4.2
Mixing rates of Markov chains
* 857
24.4.3
Practical convergence diagnostics
858
24.4.4
Accuracy of MCMC
860
24.4.5
How many chains?
862
24.5
Auxiliary variable MCMC
* 863
24.5.1
Auxiliary variable sampling for logistic regression
863
24.5.2
Slice
sampling
864
24.5.3
Swendsen Wang
866
24.5.4
Hybrid/Hamiltonian MCMC
* 868
24.6
Annealing methods
868
24.6.1
Simulated annealing
869
24.6.2
Annealed importance sampling
871
24.6.3
Parallel tempering
871
24.7
Approximating the marginal likelihood
872
24.7.1
The candidate method
872
24.7.2
Harmonic mean estimate
872
24.7.3
Annealed importance sampling
873
25
Clustering
875
25.1
Introduction
875
25.1.1
Measuring (dis)similarity
875
25.1.2
Evaluating the output of clustering methods
* 876
25.2
Dirichlet process mixture models
879
25.2.1
From finite to infinite mixture models
879
25.2.2
The Dirichlet process
882
CONTENTS xxiii
25.2.3
Applying Dirichlet processes to mixture modeling
885
25.2.4
Fitting a DP mixture model
886
25.3
Affinity propagation
887
25.4
Spectral clustering
890
25.4.1
Graph Laplacian
891
25.4.2
Normalized graph Laplacian
892
25.4.3
Example
893
25.5
Hierarchical clustering
893
25.5.1
Agglomerative clustering
895
25.5.2
Divisive clustering
898
25.5.3
Choosing the number of clusters
899
25.5.4
Bayesian hierarchical clustering
899
25.6
Clustering datapoints and features
901
25.6.1
Biclustering
903
25.6.2
Multi-view clustering
903
26
Graphical model structure learning
907
26.1
Introduction
907
26.2
Structure learning for knowledge discovery
908
26.2.1
Relevance networks
908
26.2.2
Dependency networks
909
26.3
Learning tree structures
910
26.3.1
Directed or undirected tree?
911
26.3.2
Chow-Liu algorithm for finding the ML tree structure
912
26.3.3
Finding the MAP forest
912
26.3.4
Mixtures of trees
914
26.4
Learning DAG structures
914
26.4.1
Markov equivalence
914
26.4.2
Exact structural inference
916
26.4.3
Scaling up to larger graphs
920
26.5
Learning DAG structure with latent variables
922
26.5.1
Approximating the marginal likelihood when we have missing data
922
26.5.2
Structural EM
925
26.5.3
Discovering hidden variables
926
26.5.4
Case study: Google s Rephii
928
26.5.5
Structural equation models
* 929
26.6
Learning causal DAGs
931
26.6.1
Causal interpretation of DAGs
931
26.6.2
Using causal DAGs to resolve Simpsons paradox
933
26.6.3
Learning causal DAG structures
935
26.7
Learning undirected Gaussian graphical models
938
26.7.1
MLE for a GGM
938
26.7.2
Graphical lasso
939
26.7.3
Bayesian inference for GGM structure
* 941
26.7.4
Handling non-Gaussian data using copulas
* 942
xxiv
C0NTENTS
26.8
Learning undirected discrete graphical models
942
26.8.1
Graphical lasso for MRFs/CEFs
942
26.8.2
Thin junction trees
944
27
Latent variable models for discrete data
945
27.1
Introduction
945
27.2
Distributed state LVMs for discrete data
946
27.2.1
Mixture models
946
27.2.2
Exponential family PCA
947
27.2.3
LDA and mPCA
948
27.2.4
GaP model and non-negative matrix factorization
949
27.3
Latent Dirichlet allocation {LDA)
950
27.3.1
Basics
950
27.3.2
Unsupervised discovery of topics
953
27.3.3
Quantitatively evaluating LDA as a language model
953
27.3.4
Fitting using (collapsed) Gibbs sampling
955
27.3.5
Example
956
27.3.6
Fitting using batch variational inference
957
27.3.7
Fitting using online variational inference
959
27.3.8
Determining the number of topics
960
27.4
Extensions of LDA
961
27.4.1
Correlated topic model
961
27.4.2
Dynamic topic model
962
27.4.3
LDA-HMM
963
27.4.4
Supervised LDA
967
27.5
LVMs for graph-structured data
970
27.5.1
Stochastic block model
971
27.5.2
Mixed membership stochastic block model
973
27.5.3
Relational topic model
974
27.6
LVMs for relational data
975
27.6.1
Infinite relational model
976
27.6.2
Probabilistic matrix factorization for collaborative filtering
979
27.7
Restricted Boltzmann machines (HBMs)
983
27.7.1
Varieties of RBMs
985
27.7.2
Learning RBMs
987
27.7.3
Applications of RBMs
991
28
Deep learning
995
28.1
Introduction
995
28.2
Deep generative models
995
28.2.1
Deep directed networks
996
28.2.2
Deep Boltzmann machines
996
28.2.3
Deep belief networks
997
28.2.4
Greedy layer-wise learning of DBNs
998
28.3
Deep neural networks
999
CONTENTS xxv
28.3.1
Deep multi-layer perceptrons
999
28.3.2
Deep auto-encoders
1000
28.3.3
Stacked denoising auto-encoders
1001
28.4
Applications of deep networks
1001
28.4.1
Handwritten digit classification using DBNs
1001
28.4.2
Data visualization and feature discovery using deep auto-encoders
1002
28.4.3
Information retrieval using deep auto-encoders (semantic hashing)
1003
28.4.4
Learning audio features using Id convolutional DBNs
1004
28.4.5
Learning image features using 2d convolutional DBNs
1005
28.5
Discussion
1005
Notation
1009
Bibliography
1015
Indexes
1047
Index to code
1047
Index to keywords
1050
Today s Web-enabled deluge of electronic data calls for
automated methods of data analysis. Machine learning
provides these, developing methods that can automatically
detect patterns in data and use the uncovered patterns to
predict future data.This textbook offers a comprehensive
and self-contained introduction to the field of machine
learning, a unified, probabilistic approach.
The coverage combines breadth and depth, offering
necessary background material on such topics as probabili¬
ty, optimization, and linear algebra as well as discussion of
recent developments in the field, including conditional ran¬
dom fields, L1 regularization, and deep learning.The book
is written in an informal, accessible style, complete with
pseudo-code for the most important algorithms. All topics
are copiously illustrated with color images and worked
examples drawn from such application domains as biology,
text processing, computer vision, and robotics. Rather than
providing a cookbook of different heuristic methods, the
book stresses a principled model-based approach, often
using the language of graphical models to specify mod¬
els in a concise and intuitive way. Almost all the models
described have been implemented in
a
MATLAB
software
package—PMTK (probabilistic modeling toolkit)—that is
freely available online.The book is suitable for upper-level
undergraduates with an introductory-level college math
background and beginning graduate students.
|
| any_adam_object | 1 |
| author | Murphy, Kevin P. 1970- |
| author_GND | (DE-588)1026956137 |
| author_facet | Murphy, Kevin P. 1970- |
| author_role | aut |
| author_sort | Murphy, Kevin P. 1970- |
| author_variant | k p m kp kpm |
| building | Verbundindex |
| bvnumber | BV043191702 |
| callnumber-first | Q - Science |
| callnumber-label | Q325 |
| callnumber-raw | Q325.5 |
| callnumber-search | Q325.5 |
| callnumber-sort | Q 3325.5 |
| callnumber-subject | Q - General Science |
| classification_rvk | ST 302 ST 301 ST 300 |
| classification_tum | DAT 708f |
| ctrlnum | (OCoLC)904442949 (DE-599)BVBBV043191702 |
| dewey-full | 006.3/1 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.3/1 |
| dewey-search | 006.3/1 |
| dewey-sort | 16.3 11 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV043191702 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T04:01:08Z |
| institution | BVB |
| isbn | 9780262018029 9780262305242 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028615309 |
| oclc_num | 904442949 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-573 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-473 DE-BY-UBG DE-945 DE-188 DE-523 DE-11 DE-19 DE-BY-UBM DE-29T DE-83 DE-M382 DE-20 DE-1102 DE-M347 DE-703 DE-739 DE-706 DE-862 DE-BY-FWS DE-384 DE-92 DE-1028 DE-863 DE-BY-FWS DE-1049 DE-2070s DE-634 |
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| physical | xxix, 1071 Seiten Illustrationen, Diagramme |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | The MIT Press |
| record_format | marc |
| series2 | Adaptive computation and machine learning series |
| spellingShingle | Murphy, Kevin P. 1970- Machine learning a probabilistic perspective Machine learning Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4193754-5 (DE-588)4123623-3 |
| title | Machine learning a probabilistic perspective |
| title_auth | Machine learning a probabilistic perspective |
| title_exact_search | Machine learning a probabilistic perspective |
| title_full | Machine learning a probabilistic perspective Kevin P. Murphy |
| title_fullStr | Machine learning a probabilistic perspective Kevin P. Murphy |
| title_full_unstemmed | Machine learning a probabilistic perspective Kevin P. Murphy |
| title_short | Machine learning |
| title_sort | machine learning a probabilistic perspective |
| title_sub | a probabilistic perspective |
| topic | Machine learning Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | Machine learning Probabilities Wahrscheinlichkeitstheorie Maschinelles Lernen Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028615309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028615309&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT murphykevinp machinelearningaprobabilisticperspective |
Inhaltsverzeichnis
Sonderstandort Fakultät
| Signatur: |
2000 ST 300 M978 |
|---|---|
| Exemplar 1 | nicht ausleihbar Checked out – Rückgabe bis: 31.12.2099 Vormerken |
THWS Würzburg Zentralbibliothek Lesesaal
| Signatur: |
1000 ST 302 M978 |
|---|---|
| Exemplar 1 | ausleihbar Verfügbar Bestellen |