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