Case-Based Approximate Reasoning

By: Eyke HÃ¼llermeier

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Hardcover | 23 January 2007

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390 Pages

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Case-based reasoning (CBR) has received a great deal of attention in recent years and has established itself as a core methodology in the field of artificial intelligence. The key idea of CBR is to tackle new problems by referring to similar problems that have already been solved in the past. More precisely, CBR proceeds from individual experiences in the form of cases. The generalization beyond these experiences typically relies on a kind of regularity assumption demanding that 'similar problems have similar solutions'.

Making use of different frameworks of approximate reasoning and reasoning under uncertainty, notably probabilistic and fuzzy set-based techniques, this book develops formal models of the above inference principle, which is fundamental to CBR. The case-based approximate reasoning methods thus obtained especially emphasize the heuristic nature of case-based inference and aspects of uncertainty in CBR. This way, the book contributes to a solid foundation of CBR which is grounded on formal concepts and techniques from the aforementioned fields. Besides, it establishes interesting relationships between CBR and approximate reasoning, which not only cast new light on existing methods but also enhance the development of novel approaches and hybrid systems.

This books is suitable for researchers and practioners in the fields of artifical intelligence, knowledge engineering and knowledge-based systems.

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"In the last years developments were very successful that have been based on the general concept of case-based reasoning. ... will get a lot of attention and for a good while will be the reference for many applications and further research. ... the book can be used as an excellent guideline for the implementation of problem-solving programs, but also for courses in Artificial and Computional Intelligence. Everybody who is involved in research, development and teaching in Artificial Intelligence will get something out of it." (Christian Posthoff, Zentralblatt MATH, Vol. 1119 (21), 2007)

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You Can Find This Book In

Non-Fiction Philosophy Mathematics Probability & Statistics Computing & I.T.Computer Science Artificial Intelligence Expert Systems & Knowledge-Based Systems Mathematical Theory of Computation Maths for Computer Scientists

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Published: 2nd January 2013

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Dedication	p. v
Foreword	p. xiii
Preface	p. xv
Notation	p. 1
Introduction	p. 5
Similarity and case-based reasoning	p. 5
Objective of this book	p. 6
Making case-based inference more reliable	p. 9
The important role of models	p. 10
Formal models of case-based inference	p. 11
Overview	p. 13
Similarity and Case-Based Inference	p. 17
Model-based and instance-based approaches	p. 17
Model-based approaches	p. 18
Instance-based approaches	p. 19
Knowledge representation	p. 19
Performance in generalization	p. 20
Computational complexity	p. 21
Similarity-based methods	p. 22
Nearest neighbor (NN) estimation	p. 22
Instance-based learning	p. 29
Case-based reasoning	p. 30
The concept of similarity	p. 33
Similarity in case-based reasoning	p. 33
Similarity and fuzzy sets	p. 37
Aggregation of local similarity measures	p. 38
Case-based inference	p. 41
Deterministic inference problems	p. 45
Non-deterministic inference problems	p. 48
Formal models of case-based inference	p. 52
Summary and remarks	p. 53
Constraint-Based Modeling of Case-Based Inference	p. 59
Basic concepts	p. 59
Similarity profiles and hypotheses	p. 59
Generalized similarity profiles	p. 62
Constraint-based inference	p. 65
A constraint-based inference scheme	p. 65
Non-deterministic problems	p. 69
Case-based approximation	p. 72
Properties of case-based approximation	p. 73
Local similarity profiles	p. 79
Learning similarity hypotheses	p. 81
The learning task	p. 81
A learning algorithm	p. 85
Properties of case-based learning	p. 86
Experimental results	p. 94
Application to statistical inference	p. 97
Case-based parameter estimation	p. 97
Case-based prior elicitation	p. 98
Summary and remarks	p. 99
Probabilistic Modeling of Case-Based Inference	p. 103
Basic probabilistic concepts	p. 106
Probabilistic similarity profiles and hypotheses	p. 107
Generalized probabilistic profiles	p. 110
Case-based inference, probabilistic reasoning, and statistical inference	p. 112
Learning probabilistic similarity hypotheses	p. 117
Simple hypotheses and credible case-based inference	p. 117
Extended case-based learning	p. 118
Experiments with regression and label ranking	p. 121
Regression: artificial data	p. 122
Regression: real-world data	p. 124
Label ranking	p. 126
Case-based inference as evidential reasoning	p. 129
Transformation of probabilistic evidence	p. 131
Inference from individual cases	p. 133
Combining evidence from several cases	p. 134
Assessment of cases	p. 140
Similarity-weighted approximation	p. 140
More general criteria	p. 142
Assessment of individual cases	p. 144
Complex similarity hypotheses	p. 146
Inference schemes of higher order	p. 147
Partially admissible profiles	p. 150
Approximate probabilistic inference	p. 152
Generalized uncertainty measures and profiles	p. 152
An approximate inference scheme	p. 155
Summary and remarks	p. 159
Fuzzy Set-Based Modeling of Case-Based Inference I	p. 165
Background on possibility theory	p. 165
Possibility distributions as generalized constraints	p. 166
Possibility as evidential support	p. 168
Fuzzy rule-based modeling of the CBI hypothesis	p. 169
Possibility rules	p. 170
Modeling the CBI hypothesis	p. 171
Generalized possibilistic prediction	p. 176
Control of compensation and accumulation of support	p. 177
Possibilistic support and weighted NN estimation	p. 178
Upper and lower possibility bounds	p. 179
Fuzzy logical evaluation	p. 180
Comparison of extrapolation principles	p. 181
From predictions to decisions	p. 186
An illustrative example	p. 188
Complexity issues	p. 191
Extensions of the basic model	p. 191
Dealing with incomplete information	p. 192
Discounting noisy and atypical instances	p. 194
From instances to rules	p. 198
Modified possibility rules	p. 200
Combination of several rules	p. 202
Locally restricted extrapolation	p. 204
Incorporation of background knowledge	p. 205
Experimental studies	p. 206
Preliminaries	p. 206
Classification accuracy	p. 207
Statistical assumptions and robustness	p. 209
Variation of the aggregation operator	p. 210
Representation of uncertainty	p. 211
Calibration of CBI models	p. 212
Relations to other fields	p. 219
Fuzzy and possibilistic data analysis	p. 219
Fuzzy set-based approximate reasoning	p. 222
Summary and remarks	p. 224
Fuzzy Set-Based Modeling of Case-Based Inference II	p. 229
Gradual inference rules	p. 230
The basic model	p. 230
Modification of gradual rules	p. 232
Certainty rules	p. 235
Cases as information sources	p. 239
A probabilistic model	p. 239
Combination of information sources	p. 241
Exceptionality and assessment of cases	p. 243
Local rules	p. 247
Summary and remarks	p. 249
Case-Based Decision Making	p. 253
Case-based decision theory	p. 255
Nearest Neighbor decisions	p. 258
Nearest Neighbor classification and decision making	p. 258
Nearest Neighbor decision rules	p. 260
An axiomatic characterization	p. 261
Fuzzy modeling of case-based decisions	p. 265
Basic measures for act evaluation	p. 266
Modification of the basic measures	p. 267
Interpretation of the decision criteria	p. 268
Fuzzy quantification in act evaluation	p. 270
A CBI framework of CBDM	p. 274
Generalized decision-theoretic setups	p. 274
Decision making using belief functions	p. 277
Possibilistic decision making	p. 279
CBDM models: A discussion of selected issues	p. 282
The relation between similarity, preference, and belief	p. 282
The effect of observed cases	p. 285
Dynamic aspects of decision making	p. 286
Experience-based decision making	p. 287
Compiled decision models	p. 290
Satisficing decision trees	p. 292
Experimental evaluation	p. 296
Summary and remarks	p. 301
Conclusions and Outlook	p. 307
Possibilistic Dominance in Qualitative Decisions	p. 309
Implication-Based Fuzzy Rules as Randomized Gradual Rules	p. 313
Implication-based fuzzy rules	p. 314
Gradual rules	p. 315
Other implication-based rules	p. 317
Randomized gradual rules	p. 320
A probabilistic representation of implication-based fuzzy rules	p. 322
Similarity-Based Reasoning as Logical Inference	p. 333
Simulation Results of Section 3.4.4	p. 335
Experimental Results of Section 5.5.4	p. 339
Simulation Results of Section 7.4	p. 341
Computation of an Extended Splitting Measures	p. 343
Experimental Results of Section 7.7.2	p. 345
References	p. 347
Index	p. 369
Table of Contents provided by Ingram. All Rights Reserved.

Case-Based Approximate Reasoning

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