Statistics and Neural Networks Advances at the Interface

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ISBN: 9780198524229 | 0198524226
Cover: Hardcover
Copyright: 4/6/2000

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Summary

Supplemental Materials

This book brings together some of the finest minds in the statistical andneural network research communities and provides an overview of recentdevelopments in the field of neural networks.

Contributors

xix

Flexible Discriminant and Mixture Models

(24)

Trevor Hastie

Robert Tibshirani

Andreas Buja

Introduction

(2)

Linear discriminant analysis

(3)

Reduced rank LDA

(1)

Flexible discriminant analysis

(5)

Computing the FDA model

(1)

Indicator matrix regression versus FDA

(2)

Penalised discriminant analysis

(1)

Mixture discriminant analysis

(6)

Software for fitting FDA, PDA and MDA models in S-Plus

(2)

Further extensions

(2)

References

(3)

Neural Networks for Unsupervised Learning Based on Information Theory

(40)

Jim Kay

Introduction

(2)

Some information theory

(3)

A single local processor: objective functions and learning rules

(8)

Objective functions

(2)

Single binary output

(2)

Derivation of learning rules

(2)

Discussion of the learning rules

(1)

The activation function

(1)

More complex architectures

(10)

Mutual contextual guidance

(2)

Multiple-output processors: competitive learning

(6)

Multiple-output processors: multivariate binary outputs

(2)

Global objective functions and learning rules

(3)

Local objective functions with local learning rules

(3)

Two illustrations

(4)

First experiment

(2)

Second experiment

(2)

Computational complexity

(2)

Another look at the modelling

(2)

Approximations

(1)

Acknowledgements

(1)

References

(5)

Radial Basis Function Networks and Statistics

(32)

David Lowe

Introduction

(3)

The basic RBF structure

(1)

Historical overview

(2)

Density estimation

(5)

Introduction

(1)

Semiparametric estimation of density functions

(4)

Regression

(9)

Equivalence to regularisation

(2)

Equivalence of kernel smooths and dual basis functions

(7)

Feature extraction

(8)

supervised feature extraction: discriminant analysis

(2)

Unsupervised feature extraction: nonlinear principal components

(2)

Topographic feature extraction: multidimensional scaling and Sammon mappings

(3)

Summary

(1)

Miscellaneous comments

(2)

Conclusion

(1)

References

(4)

Robust Prediction in Many-parameter Models

(32)

Nathan Intrator

The variance-bias Dilemma

(3)

Variance control via various ensemble averaging methods

100

(10)

Exhaustive training

100

(1)

Estimating the variance reduction for large ensembles

101

(1)

Noise injection

101

(9)

Integrating ensembles of estimators

110

(7)

Creating a redundant classification environment

112

(2)

Combining the hierarchy of classifiers

114

(1)

Competing rejection algorithm (CRA)

115

(1)

Results on seismic data classification

116

(1)

Bias control: imposing prior knowledge

117

(7)

Projection pursuit

117

(1)

Brief description of projection pursuit regression

118

(1)

Hybrid attempts at dimensionality reduction

119

(1)

Specific bias constraints

120

(4)

Remarks

124

(1)

References

124

(5)

Density Networks

129

(18)

David J.C. MacKay

Mark N. Gibbs

Density modelling

129

(1)

Traditional density models

129

(1)

The density network model

130

(3)

Description of the model

130

(1)

Learning in a density network

131

(1)

The derivative of the evidence with respect to w

132

(1)

Higher levels---priors on w

133

(1)

A simple Monte Carlo implementation

133

(1)

Modelling a protein family

133

(7)

Introduction

133

(1)

Regularisation schemes

134

(1)

Method for optimisation of hyperparameters

135

(1)

Toy data

136

(1)

Results on real data: globins

136

(2)

Results on real data: beta sheets

138

(2)

Future work

140

(1)

Real density networks and stochastic dynamics

140

(3)

A brief review of the hybrid Monte Carlo method

140

(1)

Demonstration on a toy real-valued dataset

141

(2)

Discussion

143

(1)

Acknowledgements

144

(1)

References

144

(3)

Latent Variable Models and Data Visualisation

147

(18)

Christopher M. Bishop

Michael E. Tipping

Introduction

147

(1)

Latent variables

148

(2)

Probabilistic principal component analysis

150

(4)

Relationship to latent variables

151

(1)

The probability model

151

(1)

Properties of the maximum-likelihood solution

152

(1)

Application to data visualisation

153

(1)

Mixtures of principal component analysers

154

(2)

EM algorithm

155

(1)

Interactive data visualisation

155

(1)

Hierarchical mixture models

156

(3)

Applications

159

(2)

Conclusions

161

(2)

Acknowledgements

163

(1)

References

163

(2)

Analysis of Latent Structure Models with Multidimensional Latent Variables

165

(30)

A.P. Dunmur

D.M. Titterington

Introduction to latent structure models

165

(2)

Latent structure models with more than one latent variable

167

(4)

Continuous latent variables---latent trait model

167

(1)

Categorical latent variables

168

(3)

Maximum likelihood estimation: general comments

171

(4)

The EM algorithm with categorical latent variables

171

(3)

Computational aspects of the E-step

174

(1)

Mean-field approximations in EM algorithms

175

(10)

General framework

175

(3)

The mean-field approximations for the latent profile example

178

(1)

The mean-field approximations for the latent class example

179

(1)

Illustration of the mean-field approximations for the latent profile model

179

(3)

An example of the application of MF to latent class models

182

(3)

Bayesian analysis of latent structure models

185

(6)

General structure and introduction to Gibbs sampling

185

(1)

Application to the multifactor latent profile model

186

(2)

Factorial hidden Markov models

188

(1)

Discussion of other models

189

(2)

Other developments in the neural-computation literature

191

(1)

Acknowledgement

192

(1)

References

192

(3)

Artificial Neural Networks and Multivariate Statistics

195

(64)

E.B. Martin

A.J. Morris

Introduction

195

(2)

Multivariate statistical approaches

197

(4)

Principal components analysis

197

(1)

Projection to latent structures (partial least squares)

198

(3)

Neural networks and their topologies

201

(8)

Static feedforward neural networks

201

(1)

Radial basis function networks

202

(1)

Dynamic neural networks

203

(4)

Wavelet networks

207

(2)

Network identification issues---data, network training and model validation

209

(4)

Plant testing and data analysis

209

(1)

Network training

209

(2)

Assessment of model validity

211

(1)

Collinearity of industrial data

212

(1)

Case study 1: spectral data calibration

213

(7)

Data description and analysis

214

(3)

Bagging regression

217

(3)

Committees of networks and neural network stacking

220

(3)

Case study 2: an application of stacked neural networks to polymer property prediction

223

(6)

Preamble

223

(1)

Inferential estimation of a quality variable

224

(5)

Applications of dynamic neural networks

229

(1)

Neural networks in state estimation

229

(1)

Nonlinear projection to latent structures

230

(3)

Preamble

230

(1)

Polynomial projection to latent structures

231

(2)

Case study 3: simulation of an industrial pH problem

233

(1)

Neural network projection to latent structres

234

(5)

Dynamic PLS modelling

239

(1)

Nonlinear principal components analysis

240

(2)

Input training network

242

(2)

Case study 4: examples using simulated data

244

(1)

Example 1: a circle

244

(1)

Example 2: a square

244

(1)

Case study 5: application of nonlinear principal components analysis for fault detection

245

(5)

An industrial materials processing unit

246

(2)

A continuous manufacturing process

248

(2)

Conclusions

250

(2)

Acknowledgements

252

(1)

References

252

(7)

Index

259

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Statistics and Neural Networks Advances at the Interface

Summary

Table of Contents

Supplemental Materials