spatial operators for evolving dynamic bayesian networks from spatio-temporal data allan tucker...
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![Page 1: Spatial Operators for Evolving Dynamic Bayesian Networks from Spatio-Temporal Data Allan Tucker Xiaohui Liu David Garway-Heath Moorfields Eye Hospital](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d4a5503460f94a26734/html5/thumbnails/1.jpg)
Spatial Operators for Evolving Dynamic Bayesian Networks from Spatio-Temporal Data
Allan TuckerXiaohui LiuDavid Garway-Heath
Moorfields Eye HospitalNHS Trust
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Contents of Talk
Introduction to BNs, DBNs, and SDBNsVisual Field DataRepresentation and Spatial OperatorsThe ExperimentsResults (Inc. Demo of the Operators)Conclusions
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BNs, DBNs and SDBNs
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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)
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Visual Field Data
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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
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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
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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}}
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Spatial Operators
Before After (a)
- - - - - - - - - - - Before After
(b)
Node x - Before Node y -Before (c)
Node x – After Node y - After
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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
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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
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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
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0 5000 10000 15000 20000 25000 30000
Function Calls
Op
erat
or
Su
cces
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AddTakeMutateSpatAddSpatCrossSpatMut
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Results – Visual Field Data
This Time All-Operators Performs BestClosely Followed by Spatial OnlyBut Given Time Non Spatial Catch UpK2 Performs Very Poorly
-112500
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0 5000 10000 15000 20000 25000 30000
Function Calls
Lo
g L
ike
lih
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dAllOps
NonSpat
Spat
K2
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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
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ResultsK2
Spatial Only
Non-Spatial Only
All Operators
K2 Non-Spat Spat All SD 119.0 142.0 122.3 129.2
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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
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Spatial Operator Demo 1
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Spatial Operator Demo 2
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Spatial Operator Demo 3
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Spatial Operator Demo 4
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Spatial Operator Demo 5
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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
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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
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Any Questions?