0 Item

Advances in Learning Theory : Methods, Models, and Applications

Methods, Models, and Applications

By: Johan A. K. Suykens (Editor), G. Horvath (Editor), S. Basu (Editor), Charles A. Micchelli (Editor), Joos Vandewalle (Editor)

Write A Review

Hardcover | 1 May 2003

At a Glance

Hardcover
440 Pages

Dimensions(cm)
23.4 x 15.6 x 2.5

Hardcover

$563.95

or 4 interest-free payments of $140.99 with

Aims to ship in 10 to 15 business days

When will this arrive by?
Enter delivery postcode to estimate

In recent years, considerable progress has been made in the understanding of problems of learning and generalization. In this context, Intelligence basically means the ability to perform well on new data after learning a model on the basis of given data. Such problems arise in many different areas and are becoming increasingly important and crucial towards many applications such as in bioinformatics, multimedia, computer vision and signal processing, internet search and information retrieval, datamining and textmining, finance, fraud detection, measurement systems and process control, and several others. Currently, the development of new technologies enables to generate massive amounts of data containing a wealth of information that remains to become explored. Often the dimensionality of the input spaces in these novel applications is huge. In the analysis of microarray data, for example, where expression levels of thousands of genes need to be analyzed given only a limited number of experiments. Without performing dimensionality reduction, the classical statistical paradigms show fundamental shortcomings at this point. Facing these new challenges, there is a need for new mathematical foundations and models such that the data can become processed in a reliable way. These subjects are very interdisciplinary and relate to problems studied in neural networks, machine learning, mathematics and statistics.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Computing & I.T.Computer Science Mathematical Theory of Computation Artificial Intelligence Machine Learning Neural Networks & Fuzzy Systems Education Education Equipment & Technology Teaching Skills & Techniques

Preface	p. v
Organizing committee	p. ix
List of chapter contributors	p. xi
An Overview of Statistical Learning Theory	p. 1
Setting of the Learning Problem	p. 2
Function estimation model	p. 2
Problem of risk minimization	p. 2
Three main learning problems	p. 2
Empirical risk minimization induction principle	p. 4
Empirical risk minimization principle and the classical methods	p. 4
Four parts of learning theory	p. 5
The Theory of Consistency of Learning Processes	p. 6
The key theorem of the learning theory	p. 6
The necessary and sufficient conditions for uniform convergence	p. 7
Three milestones in learning theory	p. 9
Bounds on the Rate of Convergence of the Learning Processes	p. 10
The structure of the growth function	p. 11
Equivalent definition of the VC dimension	p. 11
Two important examples	p. 12
Distribution independent bounds for the rate of convergence of learning processes	p. 13
Problem of constructing rigorous (distribution dependent) bounds	p. 14
Theory for Controlling the Generalization of Learning Machines	p. 15
Structural risk minimization induction principle	p. 15
Theory of Constructing Learning Algorithms	p. 17
Methods of separating hyperplanes and their generalization	p. 17
Sigmoid approximation of indicator functions and neural nets	p. 18
The optimal separating hyperplanes	p. 19
The support vector network	p. 21
Why can neural networks and support vectors networks generalize?	p. 23
Conclusion	p. 24
Best Choices for Regularization Parameters in Learning Theory: On the Bias-Variance Problem	p. 29
Introduction	p. 30
RKHS and Regularization Parameters	p. 30
Estimating the Confidence	p. 32
Estimating the Sample Error	p. 38
Choosing the optimal [gamma]	p. 40
Final Remarks	p. 41
Cucker Smale Learning Theory in Besov Spaces	p. 47
Introduction	p. 48
Cucker Smale Functional and the Peetre K-Functional	p. 48
Estimates for the CS-Functional in Anisotropic Besov Spaces	p. 52
High-dimensional Approximation by Neural Networks	p. 69
Introduction	p. 70
Variable-basis Approximation and Optimization	p. 71
Maurey-Jones-Barron's Theorem	p. 73
Variation with respect to a Set of Functions	p. 75
Rates of Approximate Optimization over Variable Basis Functions	p. 77
Comparison with Linear Approximation	p. 79
Upper Bounds on Variation	p. 80
Lower Bounds on Variation	p. 82
Rates of Approximation of Real-valued Boolean Functions	p. 83
Functional Learning through Kernels	p. 89
Some Questions Regarding Machine Learning	p. 90
r.k.h.s Perspective	p. 91
Positive kernels	p. 91
r.k.h.s and learning in the literature	p. 91
Three Principles on the Nature of the Hypothesis Set	p. 92
The learning problem	p. 92
The evaluation functional	p. 93
Continuity of the evaluation functional	p. 93
Important consequence	p. 94
IR[superscript x] the set of the pointwise defined functions on x	p. 94
Reproducing Kernel Hilbert Space (r.k.h.s)	p. 95
Kernel and Kernel Operator	p. 97
How to build r.k.h.s.?	p. 97
Carleman operator and the regularization operator	p. 98
Generalization	p. 99
Reproducing Kernel Spaces (r.k.h.s)	p. 99
Evaluation spaces	p. 99
Reproducing kernels	p. 100
Representer Theorem	p. 104
Examples	p. 105
Examples in Hilbert space	p. 105
Other examples	p. 107
Conclusion	p. 107
Leave-one-out Error and Stability of Learning Algorithms with Applications	p. 111
Introduction	p. 112
General Observations about the Leave-one-out Error	p. 113
Theoretical Attempts to Justify the Use of the Leave-one-out Error	p. 116
Early work in non-parametric statistics	p. 116
Relation to VC-theory	p. 117
Stability	p. 118
Stability of averaging techniques	p. 119
Kernel Machines	p. 119
Background on kernel machines	p. 120
Leave-one-out error for the square loss	p. 121
Bounds on the leave-one-out error and stability	p. 122
The Use of the Leave-one-out Error in Other Learning Problems	p. 123
Transduction	p. 123
Feature selection and rescaling	p. 123
Discussion	p. 124
Sensitivity analysis, stability, and learning	p. 124
Open problems	p. 124
Regularized Least-Squares Classification	p. 131
Introduction	p. 132
The RLSC Algorithm	p. 134
Previous Work	p. 135
RLSC vs. SVM	p. 136
Empirical Performance of RLSC	p. 137
Approximations to the RLSC Algorithm	p. 139
Low-rank approximations for RLSC	p. 141
Nonlinear RLSC application: image classification	p. 142
Leave-one-out Bounds for RLSC	p. 146
Support Vector Machines: Least Squares Approaches and Extensions 155	p. 155
Introduction	p. 156
Least Squares SVMs for Classification and Function Estimation	p. 158
LS-SVM classifiers and link with kernel FDA	p. 158
Function estimation case and equivalence to a regularization network solution	p. 161
Issues of sparseness and robustness	p. 161
Bayesian inference of LS-SVMs and Gaussian processes	p. 163
Primal-dual Formulations to Kernel PCA and CCA	p. 163
Kernel PCA as a one-class modelling problem and a primal-dual derivation	p. 163
A support vector machine formulation to Kernel CCA	p. 166
Large Scale Methods and On-line Learning	p. 168
Nystrom method	p. 168
Basis construction in the feature space using fixed size LS-SVM	p. 169
Recurrent Networks and Control	p. 172
Conclusions	p. 173
Extension of the [nu]-SVM Range for Classification	p. 179
Introduction	p. 180
[nu] Support Vector Classifiers	p. 181
Limitation in the Range of [nu]	p. 185
Negative Margin Minimization	p. 186
Extended [nu]-SVM	p. 188
Kernelization in the dual	p. 189
Kernelization in the primal	p. 191
Experiments	p. 191
Conclusions and Further Work	p. 194
Kernels Methods for Text Processing	p. 197
Introduction	p. 198
Overview of Kernel Methods	p. 198
From Bag of Words to Semantic Space	p. 199
Vector Space Representations	p. 201
Basic vector space model	p. 203
Generalised vector space model	p. 204
Semantic smoothing for vector space models	p. 204
Latent semantic kernels	p. 205
Semantic diffusion kernels	p. 207
Learning Semantics from Cross Language Correlations	p. 211
Hypertext	p. 215
String Matching Kernels	p. 216
Efficient computation of SSK	p. 219
n-grams- a language independent approach	p. 220
Conclusions	p. 220
An Optimization Perspective on Kernel Partial Least Squares Regression	p. 227
Introduction	p. 228
PLS Derivation	p. 229
PCA regression review	p. 229
PLS analysis	p. 231
Linear PLS	p. 232
Final regression components	p. 234
Nonlinear PLS via Kernels	p. 236
Feature space K-PLS	p. 236
Direct kernel partial least squares	p. 237
Computational Issues in K-PLS	p. 238
Comparison of Kernel Regression Methods	p. 239
Methods	p. 239
Benchmark cases	p. 240
Data preparation and parameter tuning	p. 240
Results and discussion	p. 241
Case Study for Classification with Uneven Classes	p. 243
Feature Selection with K-PLS	p. 243
Thoughts and Conclusions	p. 245
Multiclass Learning with Output Codes	p. 251
Introduction	p. 252
Margin-based Learning Algorithms	p. 253
Output Coding for Multiclass Problems	p. 257
Training Error Bounds	p. 260
Finding Good Output Codes	p. 262
Conclusions	p. 263
Bayesian Regression and Classification	p. 267
Introduction	p. 268
Least squares regression	p. 268
Regularization	p. 269
Probabilistic models	p. 269
Bayesian regression	p. 271
Support Vector Machines	p. 272
The Relevance Vector Machine	p. 273
Model specification	p. 273
The effective prior	p. 275
Inference	p. 276
Making predictions	p. 277
Properties of the marginal likelihood	p. 278
Hyperparameter optimization	p. 279
Relevance vector machines for classification	p. 280
The Relevance Vector Machine in Action	p. 281
Illustrative synthetic data: regression	p. 281
Illustrative synthetic data: classification	p. 283
Benchmark results	p. 284
Discussion	p. 285
Bayesian Field Theory: from Likelihood Fields to Hyperfields	p. 289
Introduction	p. 290
The Bayesian framework	p. 290
The basic probabilistic model	p. 290
Bayesian decision theory and predictive density	p. 291
Bayes' theorem: from prior and likelihood to the posterior	p. 293
Likelihood models	p. 295
Log-probabilities, energies, and density estimation	p. 295
Regression	p. 297
Inverse quantum theory	p. 298
Prior models	p. 299
Gaussian prior factors and approximate symmetries	p. 299
Hyperparameters and hyperfields	p. 303
Hyperpriors for hyperfields	p. 308
Auxiliary fields	p. 309
Summary	p. 312
Bayesian Smoothing and Information Geometry	p. 319
Introduction	p. 320
Problem Statement	p. 321
Probability-Based Inference	p. 322
Information-Based Inference	p. 324
Single-Case Geometry	p. 327
Average-Case Geometry	p. 331
Similar-Case Modeling	p. 332
Locally Weighted Geometry	p. 336
Concluding Remarks	p. 337
Nonparametric Prediction	p. 341
Introduction	p. 342
Prediction for Squared Error	p. 342
Prediction for 0 - 1 Loss: Pattern Recognition	p. 346
Prediction for Log Utility: Portfolio Selection	p. 348
Recent Advances in Statistical Learning Theory	p. 357
Introduction	p. 358
Problem Formulations	p. 358
Uniform convergence of empirical means	p. 358
Probably approximately correct learning	p. 360
Summary of "Classical" Results	p. 362
Fixed distribution case	p. 362
Distribution-free case	p. 364
Recent Advances	p. 365
Intermediate families of probability measures	p. 365
Learning with prior information	p. 366
Learning with Dependent Inputs	p. 367
Problem formulations	p. 367
Definition of [beta]-mixing	p. 368
UCEM and PAC learning with [beta]-mixing inputs	p. 369
Applications to Learning with Inputs Generated by a Markov Chain	p. 371
Conclusions	p. 372
Neural Networks in Measurement Systems (an engineering view)	p. 375
Introduction	p. 376
Measurement and Modeling	p. 377
Neural Networks	p. 383
Support Vector Machines	p. 389
The Nature of Knowledge, Prior Information	p. 393
Questions Concerning Implementation	p. 394
Conclusions	p. 396
List of participants	p. 403
Subject Index	p. 411
Author Index	p. 415
Table of Contents provided by Rittenhouse. All Rights Reserved.

Advances in Learning Theory : Methods, Models, and Applications

Methods, Models, and Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Machine Learning

How We Learn

The New Science of Education and the Brain

Superintelligence

Paths, Dangers, Strategies

Data Governance: The Definitive Guide

People, Processes, and Tools to Operationalize Data Trustworthiness

Prompt Engineering for Generative AI

Future-Proof Inputs for Reliable AI Outputs

Designing Large Language Model Applications

A Holistic Approach

Causal Inference in Python

Applying Causal Inference in the Tech Industry

AI Engineering

Building Applications with Foundation Models

Effective Machine Learning Teams

Best Practices for ML Practitioners

Modern Data Analytics in Excel

Using Power Query, Power Pivot and More for Enhanced Data Analytics

Analytics Engineering with SQL and Dbt

Building Meaningful Data Models at Scale

Machine Learning Interviews

Kickstart Your Machine Learning Career

Building Recommendation Systems in Python and Jax

Hands-On Production Systems at Scale

Machine Learning with Python Cookbook

2nd Edition - Practical Solutions from Preprocessing to Deep Learning

How To Think About AI A Guide For The Perplexed

A Guide For The Perplexed

A.I. Machine Learning

Architecting Data and Machine Learning Platforms

Enable Analytics and Ai-Driven Innovation in the Cloud

Intelligent Data Analytics for Solar Energy Prediction and Forecasting

Advances in Resource Assessment and PV Systems O

Machine Intelligence and Smart Systems

Third International Conference, MISS 2023, Bhopal, India, January 24-25, 2023, Revised Selected Papers, Part I

Predictive Analytics for the Modern Enterprise

A Practitioner's Guide to Designing and Implementing Solutions

Graph Neural Networks in Action

In Action

A Hands-On Introduction to Machine Learning

Graph-Powered Analytics and Machine Learning with TigerGraph

Driving Business Outcomes with Connected Data

Practical Weak Supervision

Doing More with Less Data

Less-supervised Segmentation with CNNs

Scenarios, Models and Optimization.

This product is categorised by