Antti Sorjamaa Time Series Prediction Group Bayesian Theory Chapters 2.5 – 2.8.
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Antti Sorjamaa Time Series Prediction Group Bayesian Theory Chapters 2.5 – 2.8
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Transcript of Antti Sorjamaa Time Series Prediction Group Bayesian Theory Chapters 2.5 – 2.8.
Antti SorjamaaTime Series Prediction Group
Bayesian Theory
Chapters 2.5 – 2.8
Antti Sorjamaa, TSP Group, CIS 2
OutlineOutline
Actions and UtilitiesBounds in Decision Problems
Sequential Decision ProblemsComplex Decision Problems
Inference and InformationReporting beliefs in Decision ProblemsInformation Theory
Antti Sorjamaa, TSP Group, CIS 3
2.5 Actions and Utilities2.5 Actions and Utilities
Utilities assign a numerical value for consequences through utility function
Bounds or no bounds?Conditional expected utility
Degrees of belief for events and utilitiesDecision criterion
General Utility function (Def. 2.17)
Antti Sorjamaa, TSP Group, CIS 4
2.6 Sequential Decision Problems2.6 Sequential Decision Problems
Complex decision queues broken down to simpler ones
Backward InductionOptimal stopping problem
Marriage problemSecretary problemOptimal solution close to Golden Ratio
Needed in many real life problems
Antti Sorjamaa, TSP Group, CIS 5
2.6.3 Design of Experiments2.6.3 Design of Experiments
Null experiment (standard experiment)Optimal experiment
Maximizing the Unconditional Expected Utility given the data
“If experiment not optimal, no experiment”
Value of information (Def. 2.18)Perfect Information (Def. 2.19)
Antti Sorjamaa, TSP Group, CIS 6
2.7 Inference and Information2.7 Inference and Information
Individual “knows” something, but reports (possibly) something else
Score function (utility function)Proper (Def. 2.21), honestyQuadratic (Def. 2.22), simplestLocal (Def. 2.23), weighting of mistakesLogarithmic (Def. 2.24), KL
Antti Sorjamaa, TSP Group, CIS 7
2.7 Information Theory2.7 Information Theory
KL Distance (Def. 2.30)Loss in approximation of “true beliefs”Derived from logarithmic score function
Information from data (Def. 2.26)Expected info from Experiment (Def. 2.27)
Shannon’s Expected Information
Antti Sorjamaa, TSP Group, CIS 8
2.8 Discussion2.8 Discussion
Crossing to other territoriesInformation TheoryProbability Theory
QuestionsCan all problems be viewed as inference
problems?Is there a possibility for cyclic inference
problems? Can it be solved with Bayesian?
Antti Sorjamaa, TSP Group, CIS 9
Exercises from last weekExercises from last week
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Antti Sorjamaa, TSP Group, CIS 10
Exercises from last weekExercises from last week
BlackjackActions?Events?Consequences?Preference relation to actions?
What it means?
