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

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Function Calls

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erat

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AddTakeMutateSpatAddSpatCrossSpatMut

Results – Visual Field Data

This Time All-Operators Performs BestClosely Followed by Spatial OnlyBut Given Time Non Spatial Catch UpK2 Performs Very Poorly

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Function Calls

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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

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Function Calls

Op

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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?