Uncertainty in Artificial Intelligence (eBook)

Front Cover 1
Uncertainty in Artificial Intelligence 4
Copyright Page 5
PREFACE 6
CONTRIBUTORS 8
Table of Contents 10
PART 
14 
Chapter 1. 
16 
1. Introduction 16
2. Representatiori Of Uncertain 
17 
3. Probability 18
4. Evidence Theory 20
5. Possibility Theory 24
6. Non-numeric methods 25
7. Theory of Endorsements 27
8. 
29 
9. 
32 
10. Conclusions 37
References 38
CHAPTER 
40 
1. INTRODUCTION 40
2. SOME CONSENSUS RULE CHARACTERISTICS 41
3. CHOICE OF WEIGHTS FOR LINEAR POOLS - UPDATING 43
4. CONCLUDING REMARKS 44
REFERENCES 45
PART 
46 
Chapter 3. 
48 
1. Is There An "Uncertainty Handling" Problem? 48
2. Conflation of Different Aims 49
3. Uncertainty Handling in Classification Problem Solving 52
4. Concluding Remarks 57
References 58
CHAPTER 
60 
1. INTRODUCTION 60
2. AN EXAMPLE 61
3. 'EXCHANGEABILITY' AND DOUBT ABOUT PROBABILITIES 75
4. DISCUSSION: WHEN IS PROBABILITY APPROPRIATE ? 76
REFERENCES 78
CHAPTER 
82 
1. INTRODUCTION 82
2. FORMALISMS FOR REPRESENTING UNCERTAINTY 83
3. COMPARING UIS'S 85
4. EVALUATING DIFFERENCES IN RESULTS 91
5. COMPARING PERFORMANCE ON AN EXAMPLE RULE-SET 92
6. FINAL REMARKS 94
References 95
Chapter 6. 
98 
1 Introduction 98
2 The Probabilistic Approach 99
3 Combining Evidence 102
4 "Conflicting Evidence" 106
5 Uncertain Evidence 107
6 The Fuzzy Approach 110
7 Conclusions 113
References 114
Chapter 7. 
116 
1. The Issue of Adequacy 116
2. Inference 119
REFERENCES AND RELATED PUBLICATIONS 126
CHAPTER 
130 
REFERENCES 138
CHAPTER 
140 
1. Two Probability Languages 140
2. Three Examples 142
3. Probability Judgment in Expert Systems 147
References 148
CHAPTER 10. THE INCONSISTENT USE OF MEASURES OF CERTAINTY IN ARTIFICIAL INTELLIGENCE 
150 
1. INTRODUCTION 150
2. DISTINGUISHING BELIEF UPDATES FROM ABSOLUTE BELIEFS 151
3. HISTORICAL BLURRING OF BELIEF AND BELIEF UPDATE 151
4. INTUITIVE PROPERTIES OF MEASURES OF BELIEF 152
5. PROPERTIES OF BELIEF UPDATES 154
6. A PROBABILISTIC BELIEF UPDATE 155
7. INCONSISTENCY OF EQUATING ABSOLUTE BELIEFS WITH BELIEF UPDATES 155
8. EVIDENCE COMBINATION AND MODULARITY 156
9. THE MODULAR UPDATING PARADIGM 158
10. INCONSISTENT USE OF THE MODULAR UPDATING PARADIGM 158
11. MODULAR BELIEF UPDATING IN MYCIN 159
12. MODULAR BELIEF UPDATING IN INTERNIST-1 160
13. CONSEQUENCES OF THE INCONSISTENCY 161
14. RELEVANCE OF BIASES IN THE ELICITATION OF BELIEF 162
15. SUMMARY 162
REFERENCES 163
CHAPTER 
166 
1. INTRODUCTION1: EVIDENTIAL CONFIRMATION VERSUS PROBABILITY 166
2. OVERVIEW 167
3. PROSPECTOR: BAYESIAN UPDATING WITH CONDITIONAL INDEPENDENCE 168
4. CFS ARE A TRANSFORM OF LIKELIHOOD RATIOS, WITH INDEPENDENCE ASSUMPTION 170
5. THE POINT-VALUED SPECIAL CASE OF DEMPSTER-SHAFER THEORY 171
6. COMBINING CFS IS MULTIPLYING LIKELIHOOD RATIOS IS DEMPSTER'S RULE 172
7. VIEWING EVIDENCE AS UPDATES VERSUS AS PRIORS 172
8. DISCUSSION 174
9. CONCLUSIONS 176
REFERENCES 177
CHAPTER 
180 
1. INTRODUCTION 180
2. MYCIN'S CERTAINTY FACTORS 181
3. OVERVIEW OF APPROACH 183
4. THE DESIDERATA OF CERTAINTY FACTORS 185
5. A CLOSER LOOK AT THE ORIGINAL DEFINITION 187
6. REQUIREMENT FOR A PROBABILISTIC INTERPRETATION 189
7. A PROBABILISTIC INTERPRETATION 189
8. OTHER PROBABILISTIC INTERPRETATIONS 192
9. THE ASSUMPTION OF CONDITIONAL INDEPENDENCE 193
10. SEQUENTIAL COMBINATION 196
11. NON-TREE NETWORKS 200
12. DISCUSSION 202
13. SUMMARY 203
APPENDIX 203
REFERENCES 208
CHAPTER 
210 
1. 
210 
2. COUNTEREXAMPLES 211
3. IMPOSSIBILITY OF MULTIPLE UPDATING 212
4. DISCUSSION 213
REFERENCES 214
Chapter 14. 
216 
1. Introduction 216
2. The Information-Theoretic Justification 216
3. The Axiomatic Justification 218
4. Other Methods of Reasoning with Uncertainty 220
5. Conclusion 222
References 222
CHAPTER 
224 
I. INTRODUCTION 224
II. INFORMATION, ENTROPY, AND RELATIVE-ENTROPY 224
III. THE PRINCIPLE OF MINIMUM RELATIVE ENTROPY 226
IV. RELATIVE ENTROPY AND AI 227
REFERENCES 227
CHAPTER 
230 
1. INTRODUCTION 230
2. AGGREGATION OPERATORS 232
3. LINGUISTIC VARIABLES DEFINED ON THE INTERVAL 
237 
4. DESCRIPTION OF THE EXPERIMENTS AND REQUIRED TECHNIQUES 239
5. EXPERIMENT RESULTS AND ANALYSIS 245
6. CONCLUSIONS 253
FOOTNOTES 255
REFERENCES 257
APPENDIX: PROPERTIES OF T-NORM OPERATORS 259
Chapter 17. 
262 
References 270
CHAPTER 
272 
1. OVERVIEW 272
2. UNCONDITIONAL TYPE-1 PROBABILISTIC THEORIES 275
3. CONDITIONAL TYPE-1 PROBABILISTIC THEORIES 276
4. ADDITIONAL NON-TYPE-1 ASSUMPTIONS AS CONSTRAINTS 278
5. TYPE-2 PROBABILISTIC LOGIC 279
6. EVIDENCE AND CONFIRMATION 280
7. APPLICATION OF THE PARADIGM: ENTAILMENT 281
8. APPLICATION OF THE PARADIGM: INFERENCE 284
9. DISCUSSION AND CONCLUSIONS 285
REFERENCES 288
PART 
290 
CHAPTER 
292 
The Problem 292
A New Approach: Conceptual Outline 293
Theory of Belief Functions 294
Conflict of Evidence 296
Alternative Approaches: Interdependence Versus Modularity 298
Basic 
299 
Culprits and Denials 301
Conditions for Belief Revision 302
Conflict as Control Over Revision 302
When specific revisions are not justified 303
A role for qualitative reasoning 304
Conclusion 304
Footnote 305
References 305
Chapter 20. 
308 
1. INTRODUCTION 308
2. METAPROBABILITY THEORY 308
3. DEMPSTER-SHAFER THEORY 310
4. EXPERIMENT 311
5. ANALYSIS OF EXPERIMENTAL RESULTS 314
6. CONCLUSIONS 315
REFERENCES 315
Chapter 21. 
316 
1. Introduction 316
2. Factors and Evidence 317
3. A View from Dempster-Shafer Theory 326
4. Concluding Remark 327
Reference 328
Chapter 22. 
330 
1. Introduction 330
2. A Decision Making Paradigm 330
3. Representation of State Knowledge 332
4. Decision Making with D-S Granules 334
5. Conclusion 339
References 340
PART 
342 
Chapter 23. 
344 
1. Introduction 344
2. An overview of MRS 344
3. Probabilistic databases 345
4. Forward chaining 347
5. Backward chaining 349
6. Resolution 350
7. Conclusion 350
References 351
CHAPTER 
352 
1. INTRODUCTION: MAKING DIFFICULT DECISIONS 352
2. EXPERT SYSTEMS AS DECISION AIDS 353
3. USING EXPERT SYSTEMS FOR DEVELOPING REPRESENTATIONS OF SPECIFIC DECISIONS 354
4. REPRESENTING DECISIONS AS INFLUENCE DIAGRAMS 356
5. RACHEL: A PILOT-LEVEL EXPERT DECISION ANALYST 356
6. CONCLUSION 357
REFERENCES 357
CHAPTER 25. MODEL-BASED PROBABILISTIC SITUATION IN FERENCE IN HIERARCHICAL HYPOTHESIS 
360 
1. INTRODUCTION 360
2. NUMERICAL SUPPORT FOR HYPOTHESIS HIERARCHIES 363
3. PROBABILISTIC CONFLICT RESOLUTION 366
4. SUMMARY 368
REFERENCES 368
APPENDIX A 368
CHAPTER 
370 
1. INTRODUCTION: BAYES NETWORKS AND CONSTRAINTS PROPAGATION 370
2. PROPAGATION IN SINGLY-CONNECTED NETWORKS 373
3. PROPAGATION IN MULTIPLY-CONNECTED NETWORKS 377
CONCLUSIONS 380
REFERENCES 381
CHAPTER 
384 
I. INTRODUCTION 384
2. BASIC FRAMEWORK 385
3. PROBABILISTIC INFERENCE 387
4. TRANSFORMATIONS 388
5. SOLUTION PROCEDURE 390
6. INFORMATION REQUIRED 391
7. CONCLUSIONS 394
REFERENCES 395
CHAPTER 
396 
1. INTRODUCTION 396
2. UNCERTAIN INFERENCE METHOD 397
3. COMPUTING METHODS 400
4. SUMMARY 401
REFERENCES 401
PART 
404 
CHAPTER 
406 
Introduction 406
Knowledge Sets 406
Inductive Inference 407
Updating 408
Min-score Inference with Information Updating 409
References 410
CHAPTER 
412 
1. INTRODUCTION: OVERVIEW AND MOTIVATION 412
2. 
416 
3. 
421 
4. A PROPOSAL: VIRTUAL SAMPLING 423
REFERENCES 427
Chapter 31. 
428 
Introduction 428
Rationale 429
WITT Structure 431
Implications for Applications in AI and Information 
432 
Some Results: WITT Studies 434
REFERENCES 440
CHAPTER 
442 
1. INTRODUCTION 442
2. REPRESENTATIONS FOR INDUCTIVE LEARNING 444
3. PROBABILITY AS PRODUCT OF LEARNING 447
4. PROBABILITY AS INDUCTIVE CRITERION 453
5. SUMMARY 454
REFERENCES 455
PART 
458 
CHAPTER 
460 
1. INTRODUCTION 460
2. UNCERTAINTY AS A TYPE OF KNOWLEDGE 461
3. SOME LOGICAL TYPES OF UNCERTAINTY 462
4. WEAK METHODS FOR MANAGING UNCERTAINTY 464
5. WEAK METHODS AND THE COMBINATION OF INFORMATION 466
6. META-LEVEL REASONING ABOUT UNCERTAINTY METHODS 467
REFERENCES 471
DOCUMENTATION NOTES 471
Chapter 34. 
472 
1. Interval Measures 472
2. Estimation and Decision 473
3. Secondary Criterion Solutions 475
5. Examples and Contrasts 478
6. Epistemological Considerations 481
7. Conclusion 483
Notes and References 483
CHAPTER 
486 
1. INTRODUCTION 486
2. ALGORITHMIC COMPLEXITY 489
3. A GENERAL SYSTEM FOR SOLVING PROBLEMS 491
4. USING PROBABILITY DISTRIBUTIONS TO REPRESENT KNOWLEDGE 498
5. RELATION OF ALGORITHMIC PROBABILITY TO OTHER METHODS OF DEALING WITH UNCERTAINTY 502
6. PRESENT STATE OF DEVELOPMENT OF THE SYSTEM 502
References 503
PART 
506 
CHAPTER 
508 
1. Introduction 508
2. A Pathological Game: Board Splitting 509
3. A Nonpathological Evaluation Function for Board Splitting 511
4. The Effect of F-wins 512
5. Curing Pathology by Recognizing F-wins 514
6. Conclusions and Work in Progress 516
References 517
CHAPTER 37. AN EVALUATION OF TWO ALTERNATIVES TO MINIMAX 518
1. Introduction 518
2. Results and Data Analysis 519
3. Conclusion 521
REFERENCES 521