Uncertainty in Artificial Intelligence 4 (eBook)

Front Cover 1
Uncertainty in Artificial Intelligence 4 4
Copyright Page 5
Table of Contents 8
PREFACE 6
LIST OF CONTRIBUTORS 12
Section I: CAUSAL MODELS 14
CHAPTER 1. ON THE LOGIC OF CAUSAL MODELS 16
1. INTRODUCTION AND SUMMARY OF RESULTS 16
2. SOUNDNESS AND COMPLETENESS 18
3. EXTENSIONS AND ELABORATIONS 22
ACKNOWLEDGMENT 24
REFERENCES 24
APPENDIX 26
Chapter 2. Process, Structure, and Modularity in Reasoning with Uncertainty 28
Abstract 28
1 Introduction 28
2 Related Research 29
3 Hybrid Uncertainty Management 29
4 Summary 36
References 37
Chapter 3. Probabilistic Causal Reasoning 40
Abstract 40
1 Introduction 41
2 Causal Theories 41
3 Probabilistic Projection 44
4 The Algorithm 47
5 Acquiring Rules 51
6 Conclusions 53
References 54
Chapter 4. Generating Decision Structures and Causal Explanations For Decision Making 56
ABSTRACT 56
1. INTRODUCTION 56
2. LEARNING A DECISION STRUCTURE 57
3. CAUSAL EXPLANATION IN A DETERMINISTIC UNIVERSE WITH PERFECT INFORMATION 61
4. CAUSAL EXPLANATION IN AN UNCERTAIN UNIVERSE 65
5. TESTING THE THEORY 68
6. CONCLUSIONS AND FUTURE RESEARCH 68
7. ACKNOWLEDGEMENTS 69
REFERENCES 69
Chapter 5. Control of Problem Solving: Principles and Architecture 72
1 Introduction 72
2 Decision-Theoretic Selection 73
3 The Architecture 76
4 Conclusion 79
5 Acknowledgements 80
References 80
CHAPTER 6. CAUSAL NETWORKS: SEMANTICS AND EXPRESSIVENESS 82
1. INTRODUCTION 82
2. UNDIRECTED GRAPHS 83
3. DIRECTED-ACYCLIC GRAPHS (DAGS) 84
4. FUNCTIONAL DEPENDENCIES 88
5. CONCLUSIONS 88
ACKNOWLEDGMENT 88
REFERENCES 89
Section II: UNCERTAINTY CALCULI AND COMPARISONS 90
Part 1: Uncertainty Calculi 92
CHAPTER 7. STOCHASTIC SENSITIVITY ANALYSIS USING FUZZY INFLUENCE DIAGRAMS 92
1. INTRODUCTION AND OBJECTIVE 92
2. BAYESIAN FUZZY PROBABILITIES : BASICS 94
3. FUZZY PROBABILISTIC INFERENCE 97
4. SOLVING DECISION PROBLEMS 99
5. CONCLUSIONS 102
ACKNOWLEDGEMENTS 103
REFERENCES 103
CHAPTER 8. A LINEAR APPROXIMATION METHOD FOR PROBABILISTIC INFERENCE 106
1. INTRODUCTION 106
2. NOTATION AND BASIC FRAMEWORK 108
3. VARIABLE TRANSFORMATIONS 110
4. EXPERIMENTAL OBSERVATIONS 112
5. LINEAR APPROXIMATION ALGORITHM 113
6. CONCLUSIONS 114
ACKNOWLEDGEMENTS 115
REFERENCES 115
Chapter 9. Minimum Cross Entropy Reasoning in Recursive Causal Networks 118
1 Introduction 118
2 The Principle of Minimum Cross Entropy 120
3 Recursive Causal Networks 122
4 Reasoning with Multiple Uncertain Evidence 125
5 Other Important Issues 128
6 Conclusions 129
Acknowledgement 130
References 130
CHAPTER 10. PROBABILISTIC SEMANTICS AND DEFAULTS 134
1. INTRODUCTION 134
2. WHAT'S IN A DEFAULT? 135
3. INFERENCE GRAPHS 136
4. THE FAVOURS RELATION 138
5. EXAMPLES 140
6. CONCLUSIONS 141
ACKNOWLEDGEMENTS 142
REFERENCES 142
CHAPTER 11. Modal Logics of Higher-Order Probability 146
1 Introduction 146
2 Probability as a Modal Operator 147
3 Flat Probability Models 148
4 Coherence Principles 150
5 Staged Probability Models 152
6 Relation to Modal Logic 155
7 Summary and Future Research 158
Acknowledgements 159
Notes 159
References 160
CHAPTER 12. A GENERAL NON-PROBABILISTIC THEORY OF INDUCTIVE REASONING 162
1. INTRODUCTION 162
2. THE THEORY 163
3. A COMPARISON WITH PROBABILITY THEORY 165
4. OTHER COMPARISONS 167
NOTES 169
REFERENCES 170
CHAPTER 13. EPISTEMOLOGICAL RELEVANCE AND STATISTICAL KNOWLEDGE 172
1. BACKGROUND 172
2. ASSUMPTIONS 173
3. INTERFERENCE I 175
4. INTERFERENCE II 176
5. INTERFERENCE III 177
6. DISCUSSION 178
7. INEXACT KNOWLEDGE 179
8. COMPUTATION 180
9. CONCLUSIONS 180
REFERENCES 181
CHAPTER 14. AXIOMS FOR PROBABILITY AND BELIEF-FUNCTION PROPAGATION 182
1. INTRODUCTION 182
2. SOME CONCEPTS FROM GRAPH THEORY 183
3. AN AXIOMATIC FRAMEWORK FOR LOCAL COMPUTATION 186
4. PROBABILITY PROPAGATION 202
5. BELIEF-FUNCTION PROPAGATION 207
ACKNOWLEDGEMENTS 209
REFERENCES 209
Chapter 15. A Summary of A New Normative Theory of Probabilistic Logic 212
ABSTRACT 212
What is Probabilistic Logic ? 214
New Axioms for Probabilistic Logic 215
Possible Interpretations for the Set P 216
When Must P Be Like The Real Numbers? 217
References 218
CHAPTER 16. HIERARCHICAL EVIDENCE AND BELIEF FUNCTIONS 220
1. INTRODUCTION 220
2. EXAMPLE 221
3. THREE WAYS OF DEFINING JOINT BELIEFS 223
4. SO WHICH METHOD DO I USE? 225
5. "CAVEAT MODELOR" 226
REFERENCES 227
Chapter 17. On Probability Distributions Over Possible Worlds 230
Abstract 230
1 Introduction 231
2 The Propositional Case 231
3 First-Order Languages 232
4 The Representation of Statistical Knowledge 234
5 The Representation of Defaults 236
6 Conclusions 238
7 Acknowledgement 238
References 238
Chapter 18. A Framework of Fuzzy Evidential Reasoning 240
1 Introduction 240
2 Basics of the Dempster-Shafer Theory 241
3 Previous Work 242
4 Our Approach 243
5 Conclusions 251
Acknowledgements 252
References 252
Part 2: Comparisons 254
Chapter 19. Parallel Belief Revision 254
Abstract 254
1 Introduction 254
2 Spohnian Belief Revision 255
3 Influence Diagrams and Spohnian Conditional Independence 256
4 Soundness and Completeness Results 258
5 Spohnian Networks 259
6 Updating on a Single Piece of Uncertain Evidence 260
7 Simultaneous Updating on Multiple Evidence Events 261
8 Updating on Multiple Pieces of Uncertain Evidence 263
9 Discussion 263
References 264
CHAPTER 20. EVIDENTIAL REASONING COMPARED IN A NETWORK USAGE PREDICTION TESTBED: PRELIMINARY REPORT 266
1 TESTBED 266
2 BETTING 268
3 UNCERTAINTY CALCULI 268
4 SOME PRELIMINARY DATA 271
5 BIAS OF NET FOR REPEATED CHOICES 278
6 FUTURE WORK 279
7 REFERENCES 282
Chapter 21. A Comparison of Decision Analysis and Expert Rules for Sequential Diagnosis 284
Abstract 284
1. Introduction 284
2. Decision analytic approach 286
3. Experiment 287
4. Discussion 292
5. Conclusions 293
Acknowledgements 293
References 293
Chapter 22. An Empirical Comparison of Three Inference Methods 296
1 Introduction 296
2 The Domain 297
3 The Inference Methods 297
4 The Evaluation Procedure 301
5 Utility Assessment 306
6 Details of the Experiment 308
7 Results 309
8 Discussion 311
9 Future Work 314
Acknowledgments 314
References 314
CHAPTER 23. MODELING UNCERTAIN AND VAGUE KNOWLEDGE IN POSSIBILITY AND EVIDENCE THEORIES 316
1. INTRODUCTION 316
2. REPRESENTING UNCERTAINTY 316
3. A SHORT DISCUSSION OF COX'S AXIOMATIC FRAMEWORK FOR PROBABILITY 323
4. MODELING VAGUENESS 324
CONCLUSION 329
REFERENCES 330
CHAPTER 24. PROBABILISTIC INFERENCE AND NON-MONOTONIC INFERENCE 332
1. INTRODUCTION 332
2. McCARTHY AND HAYES 333
3. NON-MONOTONIC INFERENCE 334
4. THE CANONICAL EXAMPLES 335
5. CONSISTENCY 336
6. CONCLUSIONS 338
REFERENCES 338
Chapter 25. Multiple decision trees 340
1. Introduction 340
2. Overview of ID3 341
3. Background theory 342
4. Experiments 343
5. Results 344
6. Conclusion 346
Acknowledgement 347
References 347
Section III: KNOWLEDGE ACQUISITION AND EXPLANATION 350
Chapter 26. KNET: Integrating Hypermedia and Normative Bayesian Modeling 352
Abstract 352
1. Motivation 352
2. Knowledge engineering in the Bayesian framework 356
3. Using the Bayesian model 358
4. Applications 358
5. Future work 360
Acknowledgments 361
References 361
CHAPTER 27. GENERATING EXPLANATIONS OF DECISION MODELS BASED ON AN AUGMENTED REPRESENTATION OF UNCERTAINTY 364
1. Introduction 364
2. Motivation for Using a Decision Network Model 365
3. Augmenting the Uncertainty Representation 368
4. Defining a Generic Model 370
5. Efficient Generation of Patient-Specific Models 372
6. Computer-Generated Explanation 373
7. Conclusion 376
Acknowledgements 377
References 377
Section IV: APPLICATIONS 380
CHAPTER 28. INDUCTION AND UNCERTAINTY MANAGEMENT TECHNIQUES APPLIED TO VETERINARY MEDICAL DIAGNOSIS 382
ABSTRACT 382
1.0 INTRODUCTION 382
2.1 CLASSICAL STATISTICAL METHODS 384
3.1 OVERVIEW 387
4.0 CONCLUSIONS AND FURTHER WORK 392
Acknowledgements 392
References 392
Chapter 29. Predicting the Likely Behaviors of Continuous Nonlinear Systems in Equilibrium 396
1 Introduction 396
2 Other Techniques 397
3 Simple Example Using PV R 398
4 SAB: Overview 400
5 PV R Example Revisited 401
6 SAB: Details 402
7 Discussion 405
A Some Region Probability Bounds Derivations 405
Acknowledgments 407
References 408
Chapter 30. The structure of Bayes networks for visual recognition 410
I. The problem 410
II. Nature of the vision problem 410
III. Issues in formulation 411
IV. Single verses multiply connected networks 414
V. Further directions 417
References 417
Chapter 31. Utility-Based Control for Computer Vision 420
1 Introduction 420
2 Bayesian Network for Evidential Accrual 420
3 Computing Values for Inference Actions 423
4 Control of the Dynamic Influence Diagram 426
5 Examples 427
6 Conclusions 433
7 Acknowledgments 434
References 434