1. Spatial Operators for Evolving Dynamic Bayesian Networks from Spatio-Temporal Data Allan Tucker Xiaohui Liu David Garway-Heath Moorfields Eye Hospital NHS Trust

2. Contents of Talk Introduction to BNs, DBNs, and SDBNs Visual Field Data Representation and Spatial Operators The Experiments Results (Inc. Demo of the Operators) Conclusions

3. BNs, DBNs and SDBNs

4. Visual Field Data Collected From an Extensive Study Investigating OHT VF Tests carried out approximately every month 54 Points on the VF including two on the Blind Spot 95 Patients (1809 measurements in all)

5. Visual Field Data

6. The Datasets Visual Field Data 54 Variables, 95 Patients, 1809 Time Points Synthetic Data 64 DBN Variables Representing 8x8 Grid Parents: 1 st Order Cartesian Neighbours with Time Lag of 1 Each Node has Gaussian CPT

7. Representation and Operators Population Represents the Solution Individual Represents Point in Space and its Dependencies Efficient Use of Calls to Fitness Spatial, Non-Spatial and Temporal Operators Applied to Individuals

8. Representation {{a x,a y,l}, {a x,a y,l}, {a x,a y,l}} {{a x,a y,l}, {a x,a y,l}} {{a x,a y,l}, {a x,a y,l}, {a x,a y,l}}

9. Spatial Operators

10. The Experiments Spatial Operators Only Non-Spatial Operators Only Both Sets of Operators Investigate Learning Curves (Log-Lik) and Operator Success Rate Compare to Strawman Greedy Search Investigate SD, and Expert Knowledge

11. Results – Synthetic Data Spatial Operators Only Perform the Best Non-Spatial and K2 are the Worst Non-Spatial Appears to Eventually Discover a ‘Good’ Structure

12. Results – Synthetic Data Most Successful Operator by far is SpatAdd Take, and SpatMut are also Good SpatCross Looks Bad (Few Successes’) But Accounts for Biggest Fitness Improvements

13. Results – Visual Field Data This Time All- Operators Performs Best Closely Followed by Spatial Only But Given Time Non Spatial Catch Up K2 Performs Very Poorly

14. Results – Visual Field Data Again SpatAdd, Take, and SpatMut are Best SpatCross Looks Better But Still Least Successes Again Accounts for Biggest Fitness Improvements

15. Results

17. Spatial Operator Demo 1

18. Spatial Operator Demo 2

19. Spatial Operator Demo 3

20. Spatial Operator Demo 4

21. Spatial Operator Demo 5

22. Conclusions Developed Evolutionary Operators Specifically Designed for Spatial Data Efficient Representation Perform Competitively Compared to Standard Operators on Synthetic and Real World Data Generates VF SDBNs Consistent with Experts

23. Future Work Explore Other Spatial Datasets e.g. Rainfall Investigate Other Methods Developed for Spatial NN Function – EDAs Extend the VF Model to Include Both Eyes and Clinical Information

24. Any Questions?