Bayesian networks and decision graphs:
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Edition: | 2. ed. |
| Series: | Information science and statistics
|
| Subjects: | |
| Online Access: | BTU01 FHM01 UBG01 UBY01 UBR01 Volltext Volltext Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [431] - 439 |
| Physical Description: | 1 Online-Ressource (XVI, 447 S.) graph. Darst. |
| ISBN: | 0387682813 0387682821 9780387682815 9780387682822 |
| DOI: | 10.1007/978-0-387-68282-2 |
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| 100 | 1 | |a Jensen, Finn V. |d 1945- |e Verfasser |0 (DE-588)123202752 |4 aut | |
| 245 | 1 | 0 | |a Bayesian networks and decision graphs |c Finn V. Jensen ; Thomas D. Nielsen |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a 1 Online-Ressource (XVI, 447 S.) |b graph. Darst. | ||
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| 490 | 0 | |a Information science and statistics | |
| 500 | |a Literaturverz. S. [431] - 439 | ||
| 650 | 0 | |a Bayesian statistical decision theory / Data processing | |
| 650 | 0 | |a Machine learning | |
| 650 | 0 | |a Neural networks (Computer science) | |
| 650 | 0 | |a Decision making | |
| 650 | 0 | |a Statistique bayésienne / Informatique | |
| 650 | 0 | |a Apprentissage automatique | |
| 650 | 0 | |a Réseaux neuronaux (Informatique) | |
| 650 | 0 | |a Prise de décision | |
| 650 | 4 | |a Datenverarbeitung | |
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Record in the Search Index
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| adam_text | IMAGE 1
TABLE OF CONTENTS
PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . V
1 PREREQUISITES ON PROBABILITY THEORY . . . . . . . . . . . . . . . . .
. . . . . . 1
1.1 TWO PERSPECTIVES ON PROBABILITY THEORY . . . . . . . . . . . . . . .
. . . . . 1
1.2 FUNDAMENTALS OF PROBABILITY THEORY . . . . . . . . . . . . . . . . .
. . . . . . 2
1.2.1 CONDITIONAL PROBABILITIES . . . . . . . . . . . . . . . . . . . .
. . . . . . . 4
1.2.2 PROBABILITY CALCULUS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 5
1.2.3 CONDITIONAL INDEPENDENCE . . . . . . . . . . . . . . . . . . . . .
. . . . . 6
1.3 PROBABILITY CALCULUS FOR VARIABLES . . . . . . . . . . . . . . . . .
. . . . . . . . 7
1.3.1 CALCULATIONS WITH PROBABILITY TABLES: AN EXAMPLE . . . . . 11 1.4
AN ALGEBRA OF POTENTIALS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 13
1.5 RANDOM VARIABLES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 15
1.5.1 CONTINUOUS DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . .
. . . . . . 15
1.6 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 16
PART I PROBABILISTIC GRAPHICAL MODELS
2 CAUSAL AND BAYESIAN NETWORKS . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 23
2.1 REASONING UNDER UNCERTAINTY . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 23
2.1.1 CAR START PROBLEM . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 23
2.1.2 A CAUSAL PERSPECTIVE ON THE CAR START PROBLEM . . . . . . . 24 2.2
CAUSAL NETWORKS AND D-SEPARATION . . . . . . . . . . . . . . . . . . . .
. . . . . 26
2.2.1 D-SEPARATION . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 30
2.3 BAYESIAN NETWORKS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 32
2.3.1 DEF INITION OF BAYESIAN NETWORKS . . . . . . . . . . . . . . . . .
. . . . 32
2.3.2 THE CHAIN RULE FOR BAYESIAN NETWORKS . . . . . . . . . . . . . . .
35
2.3.3 INSERTING EVIDENCE . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 39
2.3.4 CALCULATING PROBABILITIES IN PRACTICE . . . . . . . . . . . . . .
. . . 41
2.4 GRAPHICAL MODELS - FORMAL LANGUAGES FOR MODEL SPECIFICATION 42 2.5
SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 44
IMAGE 2
XII TABLE OF CONTENTS
2.6 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 45
2.7 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 45
3 BUILDING MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 51
3.1 CATCHING THE STRUCTURE . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 51
3.1.1 MILK TEST . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 52
3.1.2 COLD OR ANGINA? . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 54
3.1.3 INSEMINATION . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 55
3.1.4 A SIMPLIF IED POKER GAME . . . . . . . . . . . . . . . . . . . . .
. . . . . . 57
3.1.5 NAIVE BAYES MODELS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 58
3.1.6 CAUSALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 60
3.2 DETERMINING THE CONDITIONAL PROBABILITIES . . . . . . . . . . . . .
. . . . . 60
3.2.1 MILK TEST . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 60
3.2.2 STUD FARM . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 62
3.2.3 POKER GAME . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 66
3.2.4 TRANSMISSION OF SYMBOL STRINGS . . . . . . . . . . . . . . . . . .
. . . 68
3.2.5 COLD OR ANGINA? . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 71
3.2.6 WHY CAUSAL NETWORKS? . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 72
3.3 MODELING METHODS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 73
3.3.1 UNDIRECTED RELATIONS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 73
3.3.2 NOISY-OR . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 75
3.3.3 DIVORCING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 78
3.3.4 NOISY FUNCTIONAL DEPENDENCE . . . . . . . . . . . . . . . . . . .
. . . . 80
3.3.5 EXPERT DISAGREEMENTS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 81
3.3.6 OBJECT-ORIENTED BAYESIAN NETWORKS . . . . . . . . . . . . . . . .
. . 84
3.3.7 DYNAMIC BAYESIAN NETWORKS . . . . . . . . . . . . . . . . . . . .
. . . . 91
3.3.8 HOW TO DEAL WITH CONTINUOUS VARIABLES . . . . . . . . . . . . . .
93
3.3.9 INTERVENTIONS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 96
3.4 SPECIAL FEATURES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 97
3.4.1 JOINT PROBABILITY TABLES . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 98
3.4.2 MOST-PROBABLE EXPLANATION . . . . . . . . . . . . . . . . . . . .
. . . . . 98
3.4.3 DATA CONF LICT . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 98
3.4.4 SENSITIVITY ANALYSIS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 99
3.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 100
3.6 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 101
3.7 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 102
4 BELIEF UPDATING IN BAYESIAN NETWORKS . . . . . . . . . . . . . . . . .
. . . . 109
4.1 INTRODUCTORY EXAMPLES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 109
4.1.1 A SINGLE MARGINAL . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 110
4.1.2 DIF FERENT EVIDENCE SCENARIOS . . . . . . . . . . . . . . . . . .
. . . . . . 111
4.1.3 ALL MARGINALS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 114
4.2 GRAPH-THEORETIC REPRESENTATION . . . . . . . . . . . . . . . . . . .
. . . . . . . . 115
4.2.1 TASK AND NOTATION . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 115
4.2.2 DOMAIN GRAPHS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 116
IMAGE 3
TABLE OF CONTENTS XIII
4.3 TRIANGULATED GRAPHS AND JOIN TREES . . . . . . . . . . . . . . . . .
. . . . . . 119
4.3.1 JOIN TREES . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 122
4.4 PROPAGATION IN JUNCTION TREES . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 124
4.4.1 LAZY PROPAGATION IN JUNCTION TREES . . . . . . . . . . . . . . . .
. 127
4.5 EXPLOITING THE INFORMATION SCENARIO . . . . . . . . . . . . . . . .
. . . . . . . 130
4.5.1 BARREN NODES . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 130
4.5.2 D-SEPARATION . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 131
4.6 NONTRIANGULATED DOMAIN GRAPHS . . . . . . . . . . . . . . . . . . .
. . . . . . . 132
4.6.1 TRIANGULATION OF GRAPHS . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 134
4.6.2 TRIANGULATION OF DYNAMIC BAYESIAN NETWORKS . . . . . . . . . 137
4.7 EXACT PROPAGATION WITH BOUNDED SPACE . . . . . . . . . . . . . . . .
. . . . 140
4.7.1 RECURSIVE CONDITIONING . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 140
4.8 STOCHASTIC SIMULATION IN BAYESIAN NETWORKS . . . . . . . . . . . . .
. . . . 145
4.8.1 PROBABILISTIC LOGIC SAMPLING . . . . . . . . . . . . . . . . . . .
. . . . . 146
4.8.2 LIKELIHOOD WEIGHTING . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 148
4.8.3 GIBBS SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 150
4.9 LOOPY BELIEF PROPAGATION . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 152
4.10 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 154
4.11 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 156
4.12 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 157
5 ANALYSIS TOOLS FOR BAYESIAN NETWORKS . . . . . . . . . . . . . . . . .
. . . . 167
5.1 IEJ TREES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 168
5.2 JOINT PROBABILITIES AND A -SATURATED JUNCTION TREES . . . . . . . .
. . 169 5.2.1 A -SATURATED JUNCTION TREES . . . . . . . . . . . . . . .
. . . . . . . . . . 169
5.3 CONFIGURATION OF MAXIMAL PROBABILITY . . . . . . . . . . . . . . . .
. . . . . . 171
5.4 AXIOMS FOR PROPAGATION IN JUNCTION TREES . . . . . . . . . . . . . .
. . . . 173
5.5 DATA CONF LICT . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 174
5.5.1 INSEMINATION . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 175
5.5.2 THE CONF LICT MEASURE CONF . . . . . . . . . . . . . . . . . . . .
. . . . . . 175
5.5.3 CONF LICT OR RARE CASE . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 176
5.5.4 TRACING OF CONF LICTS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 177
5.5.5 OTHER APPROACHES TO CONF LICT DETECTION . . . . . . . . . . . . .
. 179
5.6 SE ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 179
5.6.1 EXAMPLE AND DEF INITIONS . . . . . . . . . . . . . . . . . . . . .
. . . . . . 179
5.6.2 H -SATURATED JUNCTION TREES AND SE ANALYSIS . . . . . . . . . .
182 5.7 SENSITIVITY TO PARAMETERS . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 184
5.7.1 ONE-WAY SENSITIVITY ANALYSIS . . . . . . . . . . . . . . . . . . .
. . . . 187
5.7.2 TWO-WAY SENSITIVITY ANALYSIS . . . . . . . . . . . . . . . . . . .
. . . . 188
5.8 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 188
5.9 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 190
5.10 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 191
IMAGE 4
XIV TABLE OF CONTENTS
6 PARAMETER ESTIMATION . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 195
6.1 COMPLETE DATA . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 195
6.1.1 MAXIMUM LIKELIHOOD ESTIMATION . . . . . . . . . . . . . . . . . .
. . 196
6.1.2 BAYESIAN ESTIMATION . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 197
6.2 INCOMPLETE DATA . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 200
6.2.1 APPROXIMATE PARAMETER ESTIMATION: THE EM ALGORITHM201 6.2.2 *WHY
WE CANNOT PERFORM EXACT PARAMETER ESTIMATION 207 6.3 ADAPTATION . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 207
6.3.1 FRACTIONAL UPDATING . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 210
6.3.2 FADING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 211
6.3.3 *SPECIF ICATION OF AN INITIAL SAMPLE SIZE . . . . . . . . . . . .
. . . 212
6.3.4 EXAMPLE: STRINGS OF SYMBOLS . . . . . . . . . . . . . . . . . . .
. . . . . 213
6.3.5 ADAPTATION TO STRUCTURE . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 214
6.3.6 *FRACTIONAL UPDATING AS AN APPROXIMATION . . . . . . . . . . . 215
6.4 TUNING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 218
6.4.1 EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 220
6.4.2 DETERMINING GRAD DIST( X, Y ) AS A FUNCTION OF T . . . . . . . .
222 6.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 223
6.6 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 225
6.7 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 226
7 LEARNING THE STRUCTURE OF BAYESIAN NETWORKS . . . . . . . . . . . . .
. 229
7.1 CONSTRAINT-BASED LEARNING METHODS . . . . . . . . . . . . . . . . .
. . . . . . 230
7.1.1 FROM SKELETON TO DAG . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 231
7.1.2 FROM INDEPENDENCE TESTS TO SKELETON . . . . . . . . . . . . . . .
. 234
7.1.3 EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 235
7.1.4 CONSTRAINT-BASED LEARNING ON DATA SETS . . . . . . . . . . . . .
237
7.2 OCKHAM S RAZOR . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 240
7.3 SCORE-BASED LEARNING . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 241
7.3.1 SCORE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 242
7.3.2 SEARCH PROCEDURES . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 245
7.3.3 CHOW-LIU TREES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 250
7.3.4 *BAYESIAN SCORE FUNCTIONS . . . . . . . . . . . . . . . . . . . .
. . . . . . 253
7.4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 258
7.5 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 260
7.6 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 261
8 BAYESIAN NETWORKS AS CLASSIFIERS . . . . . . . . . . . . . . . . . . .
. . . . . . . . 265
8.1 NAIVE BAYES CLASSIF IERS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 266
8.2 EVALUATION OF CLASSIF IERS . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 268
8.3 EXTENSIONS OF NAIVE BAYES CLASSIF IERS . . . . . . . . . . . . . . .
. . . . . . . . 270
8.4 CLASSIF ICATION TREES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 272
8.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 274
8.6 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 275
8.7 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 276
IMAGE 5
TABLE OF CONTENTS XV
PART II DECISION GRAPHS
9 GRAPHICAL LANGUAGES FOR SPECIFICATION OF DECISION PROBLEMS 279 9.1
ONE-SHOT DECISION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 280
9.1.1 FOLD OR CALL? . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 281
9.1.2 MILDEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 282
9.1.3 ONE DECISION IN GENERAL . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 283
9.2 UTILITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 284
9.2.1 INSTRUMENTAL RATIONALITY . . . . . . . . . . . . . . . . . . . . .
. . . . . . 287
9.3 DECISION TREES . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 290
9.3.1 A COUPLE OF EXAMPLES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 293
9.3.2 COALESCED DECISION TREES . . . . . . . . . . . . . . . . . . . . .
. . . . . . 295
9.3.3 SOLVING DECISION TREES . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 296
9.4 INFLUENCE DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 302
9.4.1 EXTENDED POKER MODEL . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 302
9.4.2 DEFINITION OF INFLUENCE DIAGRAMS . . . . . . . . . . . . . . . . .
. . . 305
9.4.3 REPETITIVE DECISION PROBLEMS . . . . . . . . . . . . . . . . . . .
. . . . 308
9.5 ASYMMETRIC DECISION PROBLEMS . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 310
9.5.1 DIF FERENT SOURCES OF ASYMMETRY . . . . . . . . . . . . . . . . .
. . . . 314
9.5.2 UNCONSTRAINED INFLUENCE DIAGRAMS . . . . . . . . . . . . . . . . .
. . 316
9.5.3 SEQUENTIAL INFLUENCE DIAGRAMS . . . . . . . . . . . . . . . . . .
. . . . 322
9.6 DECISION PROBLEMS WITH UNBOUNDED TIME HORIZONS . . . . . . . . . .
324 9.6.1 MARKOV DECISION PROCESSES . . . . . . . . . . . . . . . . . .
. . . . . . . 324
9.6.2 PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES . . . . . . . 330
9.7 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 332
9.8 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 337
9.9 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 337
10 SOLUTION METHODS FOR DECISION GRAPHS . . . . . . . . . . . . . . . .
. . . . . 343
10.1 SOLUTIONS TO INFLUENCE DIAGRAMS . . . . . . . . . . . . . . . . . .
. . . . . . . . . 343
10.1.1 THE CHAIN RULE FOR INFLUENCE DIAGRAMS . . . . . . . . . . . . . .
345
10.1.2 STRATEGIES AND EXPECTED UTILITIES . . . . . . . . . . . . . . . .
. . . . 346
10.1.3 AN EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 352
10.2 VARIABLE ELIMINATION . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 353
10.2.1 STRONG JUNCTION TREES . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 355
10.2.2 REQUIRED PAST . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 358
10.2.3 POLICY NETWORKS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 360
10.3 NODE REMOVAL AND ARC REVERSAL . . . . . . . . . . . . . . . . . . .
. . . . . . . . 362
10.3.1 NODE REMOVAL . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 362
10.3.2 ARC REVERSAL . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 363
10.3.3 AN EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 365
10.4 SOLUTIONS TO UNCONSTRAINED INFLUENCE DIAGRAMS . . . . . . . . . . .
. . . 367 10.4.1 MINIMIZING THE S-DAG . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 367
10.4.2 DETERMINING POLICIES AND STEP FUNCTIONS . . . . . . . . . . . . .
371
IMAGE 6
XVI TABLE OF CONTENTS
10.5 DECISION PROBLEMS WITHOUT A TEMPORAL ORDERING: TROUBLESHOOTING . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 373
10.5.1 ACTION SEQUENCES . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 373
10.5.2 A GREEDY APPROACH . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 375
10.5.3 CALL SERVICE . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 378
10.5.4 QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 378
10.6 SOLUTIONS TO DECISION PROBLEMS WITH UNBOUNDED TIME HORIZON 380
10.6.1 A BASIC SOLUTION . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 380
10.6.2 VALUE ITERATION . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 381
10.6.3 POLICY ITERATION . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 385
10.6.4 SOLVING PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES*388 10.7
LIMITED MEMORY INFLUENCE DIAGRAMS . . . . . . . . . . . . . . . . . . .
. . . 392
10.8 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 395
10.9 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 400
10.10EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 401
11 METHODS FOR ANALYZING DECISION PROBLEMS . . . . . . . . . . . . . . .
. . 407
11.1 VALUE OF INFORMATION . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 407
11.1.1 TEST FOR INFECTED MILK? . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 407
11.1.2 MYOPIC HYPOTHESIS-DRIVEN DATA REQUEST . . . . . . . . . . . . .
409 11.1.3 NON-UTILITY-BASED VALUE FUNCTIONS . . . . . . . . . . . . . .
. . . . 411
11.2 FINDING THE RELEVANT PAST AND FUTURE OF A DECISION PROBLEM . . 413
11.2.1 IDENTIFYING THE REQUIRED PAST . . . . . . . . . . . . . . . . . .
. . . . . 415
11.3 SENSITIVITY ANALYSIS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 420
11.3.1 EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 421
11.3.2 ONE-WAY SENSITIVITY ANALYSIS IN GENERAL . . . . . . . . . . . . .
423 11.4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 426
11.5 BIBLIOGRAPHICAL NOTES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 427
11.6 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 427
LIST OF NOTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 429
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 431
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 441
|
| any_adam_object | 1 |
| author | Jensen, Finn V. 1945- Nielsen, Thomas D. |
| author_GND | (DE-588)123202752 |
| author_facet | Jensen, Finn V. 1945- Nielsen, Thomas D. |
| author_role | aut aut |
| author_sort | Jensen, Finn V. 1945- |
| author_variant | f v j fv fvj t d n td tdn |
| building | Verbundindex |
| bvnumber | BV035462852 |
| classification_rvk | SK 830 |
| collection | ZDB-2-SCS |
| ctrlnum | (OCoLC)873592051 (DE-599)DNB981946100 |
| discipline | Informatik Mathematik |
| doi_str_mv | 10.1007/978-0-387-68282-2 |
| edition | 2. ed. |
| format | Electronic eBook |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035462852 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:35:49Z |
| institution | BVB |
| isbn | 0387682813 0387682821 9780387682815 9780387682822 |
| language | English |
| lccn | 2006938666 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017382660 |
| oclc_num | 873592051 |
| open_access_boolean | 1 |
| owner | DE-473 DE-BY-UBG DE-M347 DE-706 DE-634 DE-355 DE-BY-UBR |
| owner_facet | DE-473 DE-BY-UBG DE-M347 DE-706 DE-634 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (XVI, 447 S.) graph. Darst. |
| psigel | ZDB-2-SCS |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Information science and statistics |
| spelling | Jensen, Finn V. 1945- Verfasser (DE-588)123202752 aut Bayesian networks and decision graphs Finn V. Jensen ; Thomas D. Nielsen 2. ed. Berlin [u.a.] Springer 2007 1 Online-Ressource (XVI, 447 S.) graph. Darst. txt rdacontent c rdamedia cr rdacarrier Information science and statistics Literaturverz. S. [431] - 439 Bayesian statistical decision theory / Data processing Machine learning Neural networks (Computer science) Decision making Statistique bayésienne / Informatique Apprentissage automatique Réseaux neuronaux (Informatique) Prise de décision Datenverarbeitung Neuronales Netz (DE-588)4226127-2 gnd rswk-swf Bayes-Netz (DE-588)4567228-3 gnd rswk-swf Entscheidungsgraph (DE-588)4362839-4 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Bayes-Netz (DE-588)4567228-3 s Entscheidungsgraph (DE-588)4362839-4 s DE-604 Bayes-Entscheidungstheorie (DE-588)4144220-9 s Neuronales Netz (DE-588)4226127-2 s 1\p DE-604 Nielsen, Thomas D. Verfasser aut https://doi.org/10.1007/978-0-387-68282-2 Verlag Volltext http://www.loc.gov/catdir/enhancements/fy0823/2006938666-d.html Verlag Publisher description kostenfrei Volltext DE-576 pdf/application http://www.gbv.de/dms/bsz/toc/bsz266700578inh.pdf 2009-01-25 kostenfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017382660&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jensen, Finn V. 1945- Nielsen, Thomas D. Bayesian networks and decision graphs Bayesian statistical decision theory / Data processing Machine learning Neural networks (Computer science) Decision making Statistique bayésienne / Informatique Apprentissage automatique Réseaux neuronaux (Informatique) Prise de décision Datenverarbeitung Neuronales Netz (DE-588)4226127-2 gnd Bayes-Netz (DE-588)4567228-3 gnd Entscheidungsgraph (DE-588)4362839-4 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| subject_GND | (DE-588)4226127-2 (DE-588)4567228-3 (DE-588)4362839-4 (DE-588)4144220-9 (DE-588)4123623-3 |
| title | Bayesian networks and decision graphs |
| title_auth | Bayesian networks and decision graphs |
| title_exact_search | Bayesian networks and decision graphs |
| title_full | Bayesian networks and decision graphs Finn V. Jensen ; Thomas D. Nielsen |
| title_fullStr | Bayesian networks and decision graphs Finn V. Jensen ; Thomas D. Nielsen |
| title_full_unstemmed | Bayesian networks and decision graphs Finn V. Jensen ; Thomas D. Nielsen |
| title_short | Bayesian networks and decision graphs |
| title_sort | bayesian networks and decision graphs |
| topic | Bayesian statistical decision theory / Data processing Machine learning Neural networks (Computer science) Decision making Statistique bayésienne / Informatique Apprentissage automatique Réseaux neuronaux (Informatique) Prise de décision Datenverarbeitung Neuronales Netz (DE-588)4226127-2 gnd Bayes-Netz (DE-588)4567228-3 gnd Entscheidungsgraph (DE-588)4362839-4 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| topic_facet | Bayesian statistical decision theory / Data processing Machine learning Neural networks (Computer science) Decision making Statistique bayésienne / Informatique Apprentissage automatique Réseaux neuronaux (Informatique) Prise de décision Datenverarbeitung Neuronales Netz Bayes-Netz Entscheidungsgraph Bayes-Entscheidungstheorie Lehrbuch |
| url | https://doi.org/10.1007/978-0-387-68282-2 http://www.loc.gov/catdir/enhancements/fy0823/2006938666-d.html http://www.gbv.de/dms/bsz/toc/bsz266700578inh.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017382660&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jensenfinnv bayesiannetworksanddecisiongraphs AT nielsenthomasd bayesiannetworksanddecisiongraphs |