Applying Dempster Shafer on a Simple Graphical Network
Matthias ChanJess StigileDepartment of Electrical and Systems EngineeringWashington University in St. Louis
Advisors:Dr. Sung-Hyun Son, MIT Lincoln LaboratoryDr. Keh-Ping Dunn, MIT Lincoln LaboratoryDr. Arye Nehorai, Washington University in St. Louis
Applying Dempster-Shafer Theory on a Simple Graphical Network7 December 2010
Outline
2Speaker: Matti2Introduction3
Speaker: Matti
3Pattern Classification Formulation4
Speaker: Jess4Pattern Classification Methods
5Speaker: Jess
Notes: Supervised is labeled data, unsupervised is unlabeled5Pattern Classification Difficulties
6Speaker: Jess
Notes: Some examples Many data points/complexity of data6Graphical Model Basics
7Speaker: Matti
Notes: Nice thing about trees is that the tree is conditionally independent7Bayesian Networks8CloudyRainSprinklerWetGrass
Speaker: Matti
Notes: This example is a closed tree, but in general nodes dont need to converge8Bayesian Networks An Example
9CloudyRainSprinklerWetGrassMurphy, Kevin. An Introduction to Graphical Models. Pages 2-3. Speaker: Matti
Notes: Uses Bayes Rule and Total Probability Theorem9Inference
10Speaker: Jess
Notes: Biggest difference is that D-S gives an interval instead of one number.10Dempster Shafer Theory11
Speaker: Jess
11Dempster-Shafer Basics
12Portion of Earth that we KNOW is waterPortion of Earth that COULD be water if all of the unknown area is waterSpeaker: Jess
12Problem Statement13
Speaker: Matti
Notes: We observed those transitions13Problem Introduction14
Speaker: Jess
Notes: Notice there are 4 stages and in final stage, we have 7 states from the initial 1 state14Graphical Model
15
Speaker: Jess
15Bayes Rule
16Bayes Rule
Only 1 generation of dependence
Speaker: Matti
Note: Computationally efficient from the tree16Dempster-Shafer Example
17
Speaker: Jess
Note: We have the empty set and the set of A or B, denoted as AB17Dempster-Shafer Transitions
18
Speaker: Matti
Note: We have denoted A or B as AB18Dempster-Shafer Equations
19
Region where X13 MUST be ARegion where X13 COULD be ASpeaker: Jess
Note: Refer to problem statement paper19Conclusions
20Speaker: Matti
20Future Work
21Speaker: Jess
Notes: Weve already done some of the stuff in Matlab for Bayesian stuff21Acknowledgments
22Speaker: Jess22References
23Speaker: Matti23Questions?24