Bayesian reasoning and machine learning
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2012
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| 100 | 1 | |a Barber, David |d 1968- |e Verfasser |0 (DE-588)1014941148 |4 aut | |
| 245 | 1 | 0 | |a Bayesian reasoning and machine learning |c David Barber |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2012 | |
| 300 | |a XXIV, 697 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 0 | 7 | |a Bayes-Verfahren |0 (DE-588)4204326-8 |2 gnd |9 rswk-swf |
| 653 | |a Bayesian statistical decision theory / Data processing | ||
| 653 | |a Machine learning / Mathematics | ||
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| _version_ | 1824052728958025728 |
| adam_text | CONTENTS
Preface
xv
List of notation
xx
BRMLtoolbox
xxi
I Inference in probabilistic models
1
Probabilistic reasoning
3
1.1
Probability refresher
1.1.1
Interpreting conditional
probability
1.1.2
Probability tables
1.2
Probabilistic reasoning
1.3
Prior, likelihood and posterior
1.3.1
Two dice: what were the
individual scores?
1.4
Summary
1.5
Code
1.6
Exercises
2
Basic graph concepts
22
2.1
Graphs
2.2
Numerically encoding graphs
2.2.1
Edge list
2.2.2
Adjacency matrix
2.2.3
Clique matrix
2.3
Summary
2.4
Code
2.5
Exercises
3
Belief networks
29
3.1
The benefits of structure
3.1.1
Modelling independencies
3.1.2
Reducing the burden of
specification
3.2
Uncertain and unreliable evidence
3.2.1
Uncertain evidence
3.2.2
Unreliable evidence
3.3
Belief networks
3.3.1
Conditional independence
3.3.2
The impact of collisions
3.3.3
Graphical path manipulations
for independence
3.3.4
d-separation
3.3.5
Graphical and distributional
in/dependence
3.3.6
Markov equivalence in belief
networks
3.3.7
Belief networks have limited
expressibility
3.4
Causality
3.4.1
Simpson s paradox
3.4.2
The do-calculus
3.4.3
Influence diagrams and the
do-calculus
3.5
Summary
3.6
Code
3.7
Exercises
Graphical models
4.1
Graphical models
4.2
Markov networks
4.2.1
Markov properties
4.2.2
Markov random fields
4.2.3
Hammersley-Cliiford theorem
4.2.4
Conditional independence
using Markov networks
4.2.5
Lattice models
4.3
Chain graphical models
4.4
Factor graphs
4.4.1
Conditional independence in
factor graphs
4.5
Expressiveness of graphical
models
4.6
Summary
4.7
Code
4.8
Exercises
58
VI
Contents
5
Efficient
inference in trees
77
5.1
Marginal inference
5.1.1
Variable elimination in a
Markov chain and message
passing
5.1.2
The sum-product algorithm
on factor graphs
5.1.3
Dealing with evidence
5.1.4
Computing the marginal
likelihood
5.1.5
The problem with loops
5.2
Other forms of inference
5.2.1
Max-product
5.2.2
Finding the
N
most probable states
5.2.3
Most probable path and
shortest path
5.2.4
Mixed inference
5.3
Inference in multiply connected graphs
5.3.1
Bucket elimination
5.3.2
Loop-cut conditioning
5.4
Message passing for continuous
distributions
5.5
Summary
5.6
Code
5.7
Exercises
6
The junction tree algorithm
6.1
Clustering variables
6.1.1
Reparameterisation
6.2
Clique graphs
6.2.1
Absorption
6.2.2
Absorption schedule on
clique trees
6.3
Junction trees
6.3.1
The running intersection
property
6.4
Constructing a junction tree for
singly connected distributions
6.4.1
Morálisadon
6.4.2
Forming the clique graph
6.4.3
Forming a junction tree from
a clique graph
6.4.4
Assigning potentials to
cliques
6.5
Junction trees for multiply
connected distributions
6.5.1
Triangulation
algorithms
6.6
The junction tree algorithm
6.6
Л
Remarks on the JTA
102
6.6.2
Computing the
normalisation constant of a
distribution
6.6.3
The marginal likelihood
6.6.4
Some small JTA examples
6.6.5
Shafer-Shenoy propagation
6.7
Finding the most likely state
6.8
Reabsorption:
converting a
junction tree to a directed network
6.9
The need for approximations
6.9.1
Bounded width junction trees
6.10
Summary
6.11
Code
6.12
Exercises
Making decisions
7.1
Expected utility
7.1.1
Utility of money
7.2
Decision trees
7.3
Extending Bayesian networks
for decisions
7.3.1
Syntax of influence
diagrams
7.4
Solving influence diagrams
7.4.1
Messages on an ID
7.4.2
Using a junction tree
7.5
Markov decision processes
7.5.1
Maximising expected
utility by message passing
7.5.2
Bellman s equation
7.6
Temporally unbounded MDPs
7.6.1
Value iteration
7.6.2
Policy iteration
7.6.3
A curse of dimensionality
7.7
Variational inference and
planning
7.8
Financial matters
7.8.1
Options pricing and
expected utility
7.8.2
Binomial options pricing
model
7.8.3
Optimal investment
7.9
Further topics
7.9.1
Partially observable MDPs
7.9.2
Reinforcement learning
7.10
Summary
7.11
Code
7.12
Exercises
127
Contents
VII
II Learning in probabilistic models
8
Statistics for machine learning
165
8.1
Representing data
8.1.1
Categorical
8.1.2
Ordinal
8.1.3
Numerical
8.2
Distributions
8.2.1
The Kullback-Leibler
divergence KL(q p)
8.2.2
Entropy and information
8.3
Classical distributions
8.4
Multivariate Gaussian
8.4.1
Completing the square
8.4.2
Conditioning as system
reversal
8.4.3
Whitening and centring
8.5
Exponential family
8.5.1
Conjugate priors
8.6
Learning distributions
8.7
Properties of maximum likelihood
8.7.1
Training assuming the
correct model class
8.7.2
Training when the assumed
model is incorrect
8.7.3
Maximum likelihood and
the empirical distribution
8.8
Learning a Gaussian
8.8.1
Maximum likelihood training
8.8.2
Bayesian inference of the
mean and variance
8.8.3
Gauss-gamma distribution
8.9
Summary
8.10
Code
8.11
Exercises
9
Learning as inference
199
9.1
Learning as inference
9.1.1
Learning the bias of a coin
9.1.2
Making decisions
9.1.3
A continuum of parameters
9.1.4
Decisions based on
continuous intervals
9.2
Bayesian methods and
ML
-П
9.3
Maximum likelihood training
of belief networks
9.4
Bayesian belief network training
9.4.1
Global and local parameter
independence
9.4.2
Learning binary variable
tables using a Beta prior
9.4.3
Learning multivariate
discrete tables using a
Dirichlet prior
9.5
Structure learning
9.5.1
PC algorithm
9.5.2
Empirical independence
9.5.3
Network scoring
9.5.4
Chow-Liu trees
9.6
Maximum likelihood for
undirected models
9.6.1
The likelihood gradient
9.6.2
General tabular clique
potentials
9.6.3
Decomposable Markov
networks
9.6.4
Exponential form potentials
9.6.5
Conditional random fields
9.6.6
Pseudo
likelihood
9.6.7
Learning the structure
9.7
Summary
9.8
Code
9.9
Exercises
10
Naive
Bayes
10.1
Naive
Bayes
and conditional
independence
10.2
Estimation using maximum
likelihood
10.2.1
Binary attributes
10.2.2
Multi-state variables
10.2.3
Text classification
10.3
Bayesian naive
Bayes
10.4
Tree augmented naive
Bayes
10.4.1
Learning tree augmented
naive
Bayes
networks
10.5
Summary
10.6
Code
10.7
Exercises
11
Learning with hidden variables
11.1
Hidden variables and missing
data
11.1.1
Why hidden/missing
variables can complicate
proceedings
11.1.2
The missing at random
assumption
243
256
VIII
Contents
11
Л
.3 Maximum
likelihood
H
. 1.4
Identifiability issues
11.2
Expectation maximisation
11.2.1
Variational EM
11.2.2
Classical EM
11.2.3
Application to belief networks
11.2.4
General case
11.2.5
Convergence
11.2.6
Application to Markov
networks
11.3
Extensions of EM
11.3.1
Partial M-step
11.3.2
Partial E-step
11.4
A failure case for EM
11.5
Variational
Bayes
11.5.1
EM is a special case of
variational
Bayes
11.5.2
An example: VB for the
Asbestos-Smoking-Cancer
network
11.6
Optimising the likelihood by
gradient methods
11.6.1
Undirected models
11.7
Summary
11.8
Code
11.9
Exercises
12
Bayesian model selection
12.1
Comparing models the
Bayesian way
12.2
Illustrations: coin tossing
12.2.
1 A discrete parameter space
12.2.2
A continuous parameter
space
12.3
Occam s razor and Bayesian
complexity penalisation
12.4
A continuous example: curve
fitting
12.5
Approximating the model
likelihood
12.5.1
Laplace s method
12.5.2
Bayes
information criterion
12.6
Bayesian hypothesis testing for
outcome analysis
12.6.1
Outcome analysis
12.6.2
Нішіф:
model likelihood
12.6.3
Яяте.·
model likelihood
12.6.4
Dependent outcome analysis
12.6.5
Is classifier A better than B?
12.7
Summary
12.8
Code
12.9
Exercises
III Machine learning
284
13
Machine learning concepts
305
13.1
Styles of learning
13.1.1
S
upervised learn
і
ng
13.1.2
Unsupervised learning
13.1.3
Anomaly detection
13.1.4
Online (sequential) learning
13.1.5
Interacting with the
environment
13.1.6
Semi-supervised learning
13.2
Supervised learning
13.2.1
Utility and loss
13.2.2
Using the empirical
distribution
13.2.3
Bayesian decision approach
13.3
Bayes
versus empirical decisions
13.4
Summary
13.5
Exercises
14
Nearest neighbour classification
322
14.1
Do as your neighbour does
14.2
AT-nearest neighbours
14.3
A probabilistic interpretation of
nearest neighbours
14.3.1
When your nearest
neighbour is far away
14.4
Summary
14.5
Code
14.6
Exercises
15
Unsupervised linear dimension
reduction
329
15.1
High-dimensional spaces
-
low-dimensional manifolds
15.2
Principal components analysis
15.2.1
Deriving the optimal linear
reconstruction
15.2.2
Maximum variance
criterion
15.2.3
PCA algorithm
15.2.4
PCA and nearest
neighbours classification
15.2.5
Comments on PCA
Contents
IX
15.3
High-dimensional data
15.3.1
Eigen-decomposition for
N <
D
15.3.2
PCA via singular value
decomposition
15.4
Latent semantic analysis
15.4.1
Information retrieval
15.5
PCA with missing data
15.5.1
Finding the principal
directions
15.5.2
Collaborative filtering
using PCA with missing
data
15.6
Matrix decomposition methods
15.6.1
Probabilistic latent
semantic analysis
15.6.2
Extensions and variations
15.6.3
Applications of PLSA/NMF
15.7
Kernel PCA
15.8
Canonical correlation analysis
15.8.1
SVD
formulation
15.9
Summary
15.10
Code
15.11
Exercises
16
Supervised linear dimension
reduction
359
16.1
Supervised linear projections
16.2
Fisher s linear discriminant
16.3
Canonical
variâtes
16.3.1
Dealing with the nullspace
16.4
Summary
16.5
Code
16.6
Exercises
17
Linear models
367
17.1
Introduction: fitting a straight
line
17.2
Linear parameter models for
regression
17.2.1
Vector outputs
17.2.2
Régularisation
17.2.3
Radial basis functions
17.3
The dual representation and
kernels
17.3.1
Regression in the dual space
17.4
Linear parameter models for
classification
17.4.1
Logistic regression
Π
.4.2
Beyond first-order
gradient ascent
17.4.3
Avoiding overconfident
classification
17.4.4
Multiple classes
17.4.5
The kernel trick for
classification
17.5
Support vector machines
17.5.1
Maximum margin linear
classifier
17.5.2
Using kernels
17.5.3
Performing the optimisation
17.5.4
Probabilistic interpretation
17.6
Soft zero-one loss for outlier
robustness
17.7
Summary
17.8
Code
17.9
Exercises
18
Bayesian linear models
18.1
Regression with additive
Gaussian noise
18.1.1
Bayesian linear parameter
models
18.1.2
Determining
hyperparameters: ML-II
18.1.3
Learning the
hyperparameters using EM
18.1.4
Hyperparameter
optimisation: using the
gradient
18.1.5
Validation likelihood
18.1.6
Prediction and model
averaging
18.1.7
Sparse linear models
18.2
Classification
18.2.1
Hyperparameter optimisation
18.2.2
Laplace approximation
18.2.3
Variational Gaussian
approximation
18.2.4
Local variational
approximation
18.2.5
Relevance vector
machine for classification
18.2.6
Multi-class case
18.3
Summary
18.4
Code
18.5
Exercises
392
Contents
19
Gaussian processes
412
19.1
Non-parametric prediction
19.1.1
From parametric to
non-parametric
19.1.2
From Bayesian linear
models to Gaussian processes
19.1.3
A prior on functions
19.2
Gaussian process prediction
19.2.1
Regression with noisy
training outputs
19.3
Covariance functions
19.3.1
Making new covariance
functions from old
19.3.2
Stationary covariance
functions
19.3.3
Non-stationary
covariance functions
19.4
Analysis of covariance
functions
19.4.1
Smoothness of the functions
19.4.2
Mercer kernels
19.4.3
Fourier analysis for
stationary kernels
19.5
Gaussian processes for
classification
19.5.1
Binary classification
19.5.2
Laplace s approximation
19.5.3
Hyperparameter optimisation
19.5.4
Multiple classes
19.6
Summary
19.7
Code
19.8
Exercises
20
Mixture models
432
20.1
Density estimation using
mixtures
20.2
Expectation maximisation for
mixture models
20.2.1
Unconstrained discrete
tables
20.2.2
Mixture of product of
Bernoulli distributions
20.3
The Gaussian mixture model
20.3.1
EM algorithm
20.3.2
Practical issues
20.3.3
Classification using
Gaussian mixture models
20.3.4
The
Parzen
estimator
20.3.5
K-means
20.3.6
Bayesian mixture models
20.3.7
Semi-supervised learning
20.4
Mixture of experts
20.5
Indicator models
20.5.1
Joint indicator approach:
factorised prior
20.5.2
Polya prior
20.6
Mixed membership models
20.6.1
Latent Dirichlet allocation
20.6.2
Graph-based
representations of data
20.6.3
Dyadic data
20.6.4
Monadic data
20.6.5
Cliques and adjacency
matrices for monadic
binary data
20.7
Summary
20.8
Code
20.9
Exercises
21
Latent linear models
21.1
Factor analysis
21.1.1
Finding the optimal bias
21.2
Factor analysis: maximum
likelihood
21.2.1
Eigen-approach
likelihood optimisation
21.2.2
Expectation maximisation
21.3
Interlude: modelling faces
21.4
Probabilistic principal
components analysis
21.5
Canonical correlation analysis
and factor analysis
21.6
Independent components
analysis
21.7
Summary
21.8
Code
21.9
Exercises
22
Latent ability models
22.1
The
Rasch
model
22.1.1
Maximum likelihood
training
22.1.2
Bayesian
Rasch
models
22.2
Competition models
22.2.1
Bradley-Terry-Luce model
22.2.2
Elo
ranking model
22.2.3
Glicko and TrueSkill
462
479
Contents xi
22.3
Summary
24.2 Auto-regressive
models
22.4
Code
24.2.1
Training
an AR
model
22.5
Exercises
24.2.2 AR
model as an OLDS
24.2.3
Time-varying
AR
model
IV Dynamical models 242A Time-varying variance
-------------------------------------------------------------- AR
models
23
Discrete-State Markov models
489 24.3
Latent linear dynamical systems
23.1
Markov models
24.4
Inference
23.1.1
Equilibrium and
24ЛЛ
Filterin8
stationary distribution of 24A2 SmoothinS:
a Markov chain Rauch-Tung-Striebel
-,
ι τ
с·..·
»«ι
ji
correction method
23.1.2
Fitting Markov models
-η ι
э
w
»
rmi
ji
24.4.3
The likelihood
23.1.3
Mixture of Markov models
___...,, .-, ,, 24
A A Most likely state
23.2
Hidden Markov models
„. . , _. . .
J
,
-._.„, , . . . , 24.4.5
Time independence and
23.2.1
The classical inference
_. .
Riccati equations
problems
„. -
T
-
23.2.2
Filtering pih.Wu) 245 Leaming
Imear
dynamical systems
23.2.3
Parallel smoothing p{ht V,T) J4.5.1 ^inability issues
„ „ . _ ,. , . 24.5.2
EM algorithm
23.2.4
Correction smoothing
ь
--__„ .. , ,, .
ч
24.5.3
Subspace methods
23.2.5
Sampling from p{h1:T vl:T)
ľ
„-„,,. ... . . . 24.5.4
StructuredLDSs
23.2.6
Most likely joint state
„, „
^
-,τ.
-7
n
a-
■ 24.55
Bayesian LDSs
23.2.7
Prediction J
23.2.8
Self-localisation and 24-6 Switching auto-regressive
kidnapped robots models
23.2.9
Natural language models
1А€>Л
Inference
23.3
Learning HMMs
Ж62
Maximum
^шооа
23.3.1
EM algorithm learning using EM
23.3.2
Mixture emission 24·7 Summary
23.3.3
TheHMM-GMM 24·8 Code
23.3.4
Discriminative training
24.9
Exercises
23.4
Related models
23.4.1
Explicit duration model
25
Switching linear dynamical
23.4.2
Input-output
HMM
Systems
547
23.4.3
Linear chain CRFs
25.1
Introduction
23.4.4
Dynamic Bayesian networks
25.2
The switching LDS
23.5
Applications
25.2.1
Exact inference is
23.5.1
Object tracking computationally intractable
23.5.2
Automatic speech recognition 25.3 Gaussian sum filtering
23.5.3
Bioinformatics
25.3.1
Continuous filtering
23.5.4
Part-of-speech tagging
25.3.2
Discrete filtering
23.6
Summary
25.3.3
The likelihood
ρ(νΙ:Γ)
23.7
Code
25.3.4
Collapsing Gaussians
23.8
Exercises
25.3.5
Relation to other methods
25.4
Gaussian sum smoothing
24
ContinuOUS-State Markov models
520 25.4.1
Continuous smoothing
24.1
Observed linear dynamical 25A-2 Discrete smoothing
systems
25.4.3
Collapsing the mixture
24.1.1
Stationary distribution
^4·4
Using mixtures in smoothing
with noise
25.4.5
Relation to other methods
xii
Contents
25.5
Reset models
25.5.1
A Poisson
reset model
25.5.2
Reset-HMM-LDS
25.6
Summary
25.7
Code
25.8
Exercises
26
Distributed computation
568
26.1
Introduction
26.2
Stochastic Hopfield networks
26.3
Learning sequences
26.3.1
A single sequence
26.3.2
Multiple sequences
26.3.3
Boolean networks
26.3.4
Sequence disambiguation
26.4
Tractable continuous latent
variable models
26.4.1
Deterministic latent variables
26.4.2
An augmented Hopfield
network
26.5
Neural models
26.5.1
Stochastically spiking
neurons
26.5.2
Hopfield membrane
potential
26.5.3
Dynamic synapses
26.5.4
Leaky integrate and fire
models
26.6
Summary
26.7
Code
26.8
Exercises
V Approximate inference
27
Sampling
587
27.1
Introduction
27.1.1
Univariate sampling
27.1.2
Rejection sampling
27.1.3
Multivariate sampling
27.2
Ancestral sampling
27.2.1
Dealing with evidence
27.2.2
Perfect sampling for a
Markov network
27.3
Gibbs sampling
27.3.1
Gibbs sampling as a
Markov chain
27.3.2
Structured Gibbs sampling
27.3.3
Remarks
27.4
Markov chain Monte Carlo (MCMC)
27.4.1
Markov chains
27.4.2
Metropolis-Hastings
sampling
27.5
Auxiliary variable methods
27.5.1
Hybrid Monte Carlo (HMC)
27.5.2
Swendson-Wang (SW)
27.5.3
Slice sampling
27.6
Importance sampling
27.6.1
Sequential importance
sampling
27.6.2
Particle filtering as an
approximate forward pass
27.7
Summary
27.8
Code
27.9
Exercises
28
Deterministic approximate
inference
617
28.1
Introduction
28.2
The Laplace approximation
28.3
Properties of Kullback-
Leibler variational inference
28.3.1
Bounding the
normalisation constant
28.3.2
Bounding the marginal
likelihood
28.3.3
Bounding marginal
quantities
28.3.4
Gaussian approximations
using KL divergence
28.3.5
Marginal and moment
matching properties of
minimising KL(p q)
28.4
Variational bounding using KL(q p)
28.4.1
Pairwise Markov random field
28.4.2
General mean-field equations
28.4.3
Asynchronous updating
guarantees approximation
improvement
28.4.4
Structured variational
approximation
28.5
Local and KL variational
approximations
28.5.1
Local approximation
28.5.2
KL variational
approximation
28.6
Mutual information
maximisation: a KL
variational approach
Contents
XIII
28.6.1 The
information
maximisation algorithm
28.6.2
Linear Gaussian decoder
28.7
Loopy belief propagation
28.7.1
Classical BP on an
undirected graph
28.7.2
Loopy BP as a variational
procedure
28.8
Expectation propagation
28.9
MAP for Markov networks
28.9.1
Pairwise Markov networks
28.9.2
Attractive binary Markov
networks
28.9.3
Potts model
28.10
Further reading
28.11
Summary
28.12
Code
28.13
Exercises
Appendix A: Background mathematics
655
A.I Linear algebra
A.
2
Multivariate calculus
A.3 Inequalities
A.4 Optimisation
A.5 Multivariate optimisation
A.6 Constrained optimisation
using
Lagrange
multipliers
References
675
Index
689
Colour plate section between pp.
360
and
361
|
| any_adam_object | 1 |
| author | Barber, David 1968- |
| author_GND | (DE-588)1014941148 |
| author_facet | Barber, David 1968- |
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| ctrlnum | (OCoLC)778803579 (DE-599)BSZ339421207 |
| discipline | Informatik Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV039953933 |
| illustrated | Illustrated |
| indexdate | 2025-02-14T17:56:55Z |
| institution | BVB |
| isbn | 9780521518147 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024811811 |
| oclc_num | 778803579 |
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| owner | DE-11 DE-91G DE-BY-TUM DE-703 DE-824 DE-473 DE-BY-UBG DE-634 DE-20 DE-83 DE-739 DE-706 |
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| physical | XXIV, 697 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Barber, David 1968- Bayesian reasoning and machine learning Datenverarbeitung Mathematik Datenaufbereitung (DE-588)4148865-9 gnd Mathematik (DE-588)4037944-9 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| subject_GND | (DE-588)4148865-9 (DE-588)4037944-9 (DE-588)4193754-5 (DE-588)4204326-8 |
| title | Bayesian reasoning and machine learning |
| title_auth | Bayesian reasoning and machine learning |
| title_exact_search | Bayesian reasoning and machine learning |
| title_full | Bayesian reasoning and machine learning David Barber |
| title_fullStr | Bayesian reasoning and machine learning David Barber |
| title_full_unstemmed | Bayesian reasoning and machine learning David Barber |
| title_short | Bayesian reasoning and machine learning |
| title_sort | bayesian reasoning and machine learning |
| topic | Datenverarbeitung Mathematik Datenaufbereitung (DE-588)4148865-9 gnd Mathematik (DE-588)4037944-9 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| topic_facet | Datenverarbeitung Mathematik Datenaufbereitung Maschinelles Lernen Bayes-Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024811811&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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