spatial operators for evolving dynamic bayesian networks from spatio-temporal data
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Spatial Operators for Evolving Dynamic Bayesian Networks from Spatio-Temporal Data
Allan TuckerXiaohui LiuDavid Garway-Heath
Moorfields Eye HospitalNHS Trust
Contents of Talk
Introduction to BNs, DBNs, and SDBNsVisual Field DataRepresentation and Spatial OperatorsThe ExperimentsResults (Inc. Demo of the Operators)Conclusions
BNs, DBNs and SDBNs
Visual Field Data
Collected From an Extensive StudyInvestigating OHTVF Tests carried out approximately every month54 Points on the VF including two on the Blind Spot95 Patients (1809 measurements in all)
Visual Field Data
The Datasets
Visual Field Data 54 Variables, 95 Patients, 1809 Time
Points
Synthetic Data 64 DBN Variables Representing 8x8 Grid Parents: 1st Order Cartesian Neighbours
with Time Lag of 1 Each Node has Gaussian CPT
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
Representation{{ax,ay,l}, {ax,ay,l}, {ax,ay,l}}
{{ax,ay,l}, {ax,ay,l}}
{{ax,ay,l}, {ax,ay,l}, {ax,ay,l}}
Spatial Operators
Before After (a)
- - - - - - - - - - - Before After
(b)
Node x - Before Node y -Before (c)
Node x – After Node y - After
The Experiments
Spatial Operators OnlyNon-Spatial Operators OnlyBoth Sets of OperatorsInvestigate Learning Curves (Log-Lik) and Operator Success RateCompare to Strawman Greedy SearchInvestigate SD, and Expert Knowledge
Results – Synthetic Data
Spatial Operators Only Perform the BestNon-Spatial and K2 are the WorstNon-Spatial Appears to Eventually Discover a ‘Good’ Structure
-178000-177900-177800-177700-177600-177500-177400-177300-177200-177100-177000
0 5000 10000 15000 20000 25000 30000
Function Calls
Lo
g L
ikel
iho
od
AllOps
NonSpat
Spat
K2
Results – Synthetic Data
Most Successful Operator by far is SpatAddTake, and SpatMut are also GoodSpatCross Looks Bad (Few Successes’)But Accounts for Biggest Fitness Improvements
0
10
20
30
40
50
60
70
80
0 5000 10000 15000 20000 25000 30000
Function Calls
Op
erat
or
Su
cces
es
AddTakeMutateSpatAddSpatCrossSpatMut
Results – Visual Field Data
This Time All-Operators Performs BestClosely Followed by Spatial OnlyBut Given Time Non Spatial Catch UpK2 Performs Very Poorly
-112500
-112000
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-111000
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-110000
0 5000 10000 15000 20000 25000 30000
Function Calls
Lo
g L
ike
lih
oo
dAllOps
NonSpat
Spat
K2
Results – Visual Field Data
Again SpatAdd, Take, and SpatMut are BestSpatCross Looks Better But Still Least SuccessesAgain Accounts for Biggest Fitness Improvements
0102030405060708090100
0 5000 10000 15000 20000 25000 30000
Function Calls
Op
erat
or
Su
cces
ses
AddTakeMutateSpatAddSpatCrossSpatMut
ResultsK2
Spatial Only
Non-Spatial Only
All Operators
K2 Non-Spat Spat All SD 119.0 142.0 122.3 129.2
ResultsK2
Spatial Only
Non-Spatial Only
All Operators
% Links in
same Bundle Mean
ON Distance K2 62.963 41.056
Non-Spat 70.863 29.477 Spat 78.325 19.225 All 73.333 25.138
Spatial Operator Demo 1
Spatial Operator Demo 2
Spatial Operator Demo 3
Spatial Operator Demo 4
Spatial Operator Demo 5
Conclusions
Developed Evolutionary Operators Specifically Designed for Spatial DataEfficient RepresentationPerform Competitively Compared to Standard Operators on Synthetic and Real World DataGenerates VF SDBNs Consistent with Experts
Future Work
Explore Other Spatial Datasets e.g. RainfallInvestigate Other Methods Developed for Spatial NN Function – EDAsExtend the VF Model to Include Both Eyes and Clinical Information
Any Questions?
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