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Model Choice and Model Aggregation [Mīkstie vāki]

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  • Formāts: Paperback / softback, 372 pages, height x width x depth: 239x157x20 mm, weight: 567 g
  • Izdošanas datums: 27-Sep-2017
  • Izdevniecība: Editions Technip
  • ISBN-10: 2710811774
  • ISBN-13: 9782710811770
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Model Choice and Model AggregationPalielināt
  • Formāts: Paperback / softback, 372 pages, height x width x depth: 239x157x20 mm, weight: 567 g
  • Izdošanas datums: 27-Sep-2017
  • Izdevniecība: Editions Technip
  • ISBN-10: 2710811774
  • ISBN-13: 9782710811770
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9782710811770.html
1 A Model Selection Tale 1(20)
Jean-Jacques Droesbeke
Gilbert Saporta
Christine Thomas-Agnan
1.1 Introduction
1(1)
1.2 Elements of the history of words and ideas
1(1)
1.3 Modeling in astronomy
2(3)
1.4 Triangulation in geodesy
5(2)
1.5 The measurement of meridian arcs
7(3)
1.6 A model selection tale
10(4)
1.7 A new model appears
14(3)
1.8 Expeditions for choosing a good model
17(1)
1.9 The control of errors
18(1)
1.10 A final example
18(2)
1.11 Outline of the book
20(1)
2 Model's Introduction 21(50)
Pascal Massart
2.1 Model selection
22(8)
2.1.1 Empirical risk minimization
23(3)
2.1.2 The model choice paradigm
26(1)
2.1.3 Model selection via penalization
27(3)
2.2 Selection of linear Gaussian models
30(5)
2.2.1 Examples of Gaussian frameworks
31(2)
2.2.2 Some model selection problems
33(2)
2.2.3 The least squares procedure
35(1)
2.3 Selecting linear models
35(8)
2.3.1 Mallows' heuristics
37(1)
2.3.2 Schwarz's heuristics
37(1)
2.3.3 A first model selection theorem for linear models
38(5)
2.4 Adaptive estimation in the minimax sense
43(18)
2.4.1 Minimax lower bounds
45(9)
2.4.2 Adaptive properties of penalized estimators for Gaussian sequences
54(1)
2.4.3 Adaptation with respect to ellipsoids
55(1)
2.4.4 Adaptation with respect to arbitrary lp-bodies
56(5)
2.5 Appendix
61(10)
2.5.1 Functional analysis: from function spaces to sequence spaces
61(2)
2.5.2 Gaussian processes
63(8)
3 Non Linear Gaussian Model Selection 71(30)
Pascal Massart
3.1 A general Theorem
71(5)
3.2 Selecting ellipsoids and l2 regularization
76(8)
3.2.1 Adaptation over Besov ellipsoids
77(2)
3.2.2 A first penalization strategy
79(2)
3.2.3 l2 regularization
81(3)
3.3 l1 regularization
84(3)
3.3.1 Variable selection
85(1)
3.3.2 Selecting l1 balls and the Lasso
86(1)
3.4 Appendix
87(14)
3.4.1 Concentration inequalities
87(9)
3.4.2 Information inequalities
96(2)
3.4.3 Birge's Lemma
98(3)
4 Bayesian Model Choice 101(20)
Jean-Michel Marin
Christian Robert
4.1 The Bayesian paradigm
101(6)
4.1.1 The posterior distribution
101(3)
4.1.2 Bayesian estimates
104(1)
4.1.3 Conjugate prior distributions
104(1)
4.1.4 Noninformative priors
105(1)
4.1.5 Bayesian credible sets
106(1)
4.2 Bayesian discrimination between models
107(6)
4.2.1 The model index as a parameter
107(2)
4.2.2 The Bayes Factor
109(1)
4.2.3 The ban on improper priors
110(2)
4.2.4 The Bayesian Information Criterium
112(1)
4.2.5 Bayesian Model Averaging
113(1)
4.3 The case of linear regression models
113(8)
4.3.1 Conjugate prior
114(1)
4.3.2 Zellner's G prior distribution
114(3)
4.3.3 HPD regions
117(1)
4.3.4 Calculation of evidences and Bayes factors
117(1)
4.3.5 Variable Selection
118(3)
5 Some Computational Aspects Of Bayesian Model Choice 121(14)
Jean-Michel Marin
Christian Robert
5.1 Some Monte Carlo strategies to approximate the evidence
121(6)
5.1.1 The basic Monte Carlo solution
123(1)
5.1.2 Usual importance sampling approximations
124(2)
5.1.3 The Harmonic mean approximation
126(1)
5.1.4 The Chib's method
127(1)
5.2 The bridge sampling methodology to compare embedded models
127(3)
5.3 A Monte Carlo Markov Chain method for variable selection
130(5)
5.3.1 The Gibbs sampler
130(3)
5.3.2 A Stochastic Search for the Most Likely Model
133(2)
6 Randomization And Aggregation For Predictive Modeling With Classification Data 135(30)
Nicolas Vayatis
6.1 Motivations
135(1)
6.2 Randomness, bless our data!
136(6)
6.2.1 A probabilistic view of classification data
136(4)
6.2.2 Let the data go: error estimation and model validation
140(2)
6.3 Power to the masses: aggregation principles
142(8)
6.3.1 Voting and averaging in binary classification
142(1)
6.3.2 A lazy way to multi-class classification
143(1)
6.3.3 Agreement and averaging in the context of scoring
144(4)
6.3.4 From bipartite ranking to K-partite ranking
148(2)
6.4 Time for doers: popular aggregation meta-algorithms
150(7)
6.4.1 Bagging
151(1)
6.4.2 Boosting
152(2)
6.4.3 Forests for bipartite ranking and scoring
154(3)
6.5 Time for thinkers: Theory of aggregated rules
157(8)
6.5.1 Aggregation of classification rules
157(1)
6.5.2 Consistency of Forests
158(2)
6.5.3 From bipartite consistency to K-partite consistency
160(5)
7 Mixture Models 165(72)
Christophe Biernacki
7.1 Mixture models as a many-purpose tool
165(10)
7.1.1 Starting from applications
165(3)
7.1.2 The mixture model answer
168(2)
7.1.3 Classical mixture models
170(5)
7.1.4 Other models
175(1)
7.2 Estimation
175(11)
7.2.1 Overview
175(1)
7.2.2 Maximum likelihood and variants
176(3)
7.2.3 Theoretical difficulties related to the likelihood
179(1)
7.2.4 Estimation algorithms
180(6)
7.3 Model selection in density estimation
186(14)
7.3.1 Need to select a model
186(3)
7.3.2 Frequentist approach and deviance
189(5)
7.3.3 Bayesian approach and integrated likelihood
194(6)
7.4 Model selection in (semi-)supervised classification
200(8)
7.4.1 Need to select a model
200(3)
7.4.2 Error rates-based criteria
203(2)
7.4.3 A predictive deviance criterion
205(3)
7.5 Model selection in clustering
208(9)
7.5.1 Need to select a model
208(1)
7.5.2 Partition-based criteria
209(2)
7.5.3 The Integrated Completed Likelihood criterion
211(6)
7.6 Experiments on real data sets
217(17)
7.6.1 BIC: extra-solar planets
218(1)
7.6.2 AICcond/BIC/AIC/BEC/ecv: benchmark data sets
219(2)
7.6.3 AICcond/ecvV: textile data set
221(1)
7.6.4 BIC: social comparison theory
222(2)
7.6.5 NEC: marketing data
224(1)
7.6.6 ICL: prostate cancer data
225(3)
7.6.7 BIC: density estimation in the steel industry
228(1)
7.6.8 BIC: partitioning communes of Wallonia
229(2)
7.6.9 ICLbic/BIC: acoustic emission control
231(1)
7.6.10 ICLbic/ICL/BIC/ILbayes: a seabird data set
232(2)
7.7 Future methodological challenges
234(3)
8 Calibration Of Penalties 237(10)
Pascal Massart
8.1 The concept of minimal penalty
238(5)
8.1.1 A small number of models
239(3)
8.1.2 A large number of models
242(1)
8.2 Data-driven penalties
243(4)
8.2.1 From theory to practice
243(1)
8.2.2 The slope heuristics
244(3)
9 High Dimensional Clustering 247(36)
Christophe Biernacki
Cathy Maugis-Rabusseau
9.1 Introduction
247(3)
9.2 HD clustering: Curse or blessing?
250(6)
9.2.1 HD density estimation: Curse
250(2)
9.2.2 HD clustering: A mix of curse and blessing
252(2)
9.2.3 Intermediate conclusion
254(2)
9.3 Non-canonical models
256(6)
9.3.1 Gaussian mixture of factor analysers
256(1)
9.3.2 HD Gaussian mixture models
257(1)
9.3.3 Functional data
258(4)
9.3.4 Intermediate conclusion
262(1)
9.4 Canonical models
262(20)
9.4.1 Parsimonious mixture models
263(3)
9.4.2 Variable selection through regularization
266(4)
9.4.3 Variable role modelling
270(4)
9.4.4 Co-clustering
274(7)
9.4.5 Intermediate conclusion
281(1)
9.5 Future methodological challenges
282(1)
10 Clustering Of Co-Expressed Genes 283(30)
Marie-Laure Martin-Magniette
Cathy Maugis-Rabusseau
Andrea Rau
10.1 Introduction
283(1)
10.2 Model-based clustering
284(2)
10.3 Clustering of microarray data
286(10)
10.3.1 Microarray data
286(1)
10.3.2 Gaussian mixture models
287(1)
10.3.3 Application
288(8)
10.4 Clustering of RNA-seq data
296(11)
10.4.1 RNA-seq data
296(1)
10.4.2 Poisson mixture models
297(2)
10.4.3 Applications
299(8)
10.5 Conclusion
307(6)
11 Forecasting The French National Electricity Consumption: From Sparse Models To Aggregated Forecasts 313(14)
Mathilde Mougeot
11.1 Functional regression models
315(2)
11.2 Data Mining using sparse approximation of the intra day load curves
317(3)
11.2.1 Choice of a generic dictionary
318(1)
11.2.2 Mining and clustering
319(1)
11.2.3 Patterns of consumption
320(1)
11.3 Sparse modeling with adaptive dictionaries
320(1)
11.4 Forecasting
321(2)
11.4.1 The experts
322(1)
11.4.2 Aggregation
322(1)
11.5 Performances & Software
323(1)
11.6 Conclusion and perspectives
324(1)
11.7 Annexes
325(2)
Bibliography 327(26)
Index 353