UNCERTML - DESCRIBING AND COMMUNICATING UNCERTAINTY

Matthew Williamswilliamw@aston.ac.uk

OVERVIEW Introduction.

Motivation – the Semantic and Sensor Webs.

UncertML overview.

Use case – The INTAMAP project.

Conclusions.

MOTIVATIONThe semantic and sensor webs

THE SENSOR WEB

SENSOR WEB ENABLEMENT (SWE) Open Geospatial Consortium (OGC) initiative

Interoperability interfaces and metadata encodings.

Real time integration of heterogeneous sensor webs into the information infrastructure.

Current SWE standards Observations & Measurements SensorML SWE Common

No formal standard for quantifying uncertainty

<Quantity id="elevationAngle" fixed="false" definition="urn:ogc:def:scanElevationAngle">

<uom xlink:href="urn:ogc:unit:degree"/><quality><Tolerance definition="urn:ogc:def:tolerance2std"><value> -0.02 0.02 </value>

</Tolerance></quality><value> 25.3 </value>

</Quantity>

HOW UNCERTAINTY IS USED WITHIN THE SEMANTIC WEB

PR-OWL: a Bayesian Ontology Language for the Semantic Web: Extends OWL to allow probabilistic knowledge to

be represented in an ontology. Used for reasoning with Bayesian inference. Random variables are described by either a PR-

OWL table (discrete probability) or using a proprietary format.

Other standards looking at similar concepts: BayesOWL. FuzzyOWL.

What next?

A formal open standard for quantifying complex uncertainties Extend to allow continuous distributions More powerful reasoning, richer representations

UNCERTML

OVERVIEW

Split into three distinct packages (distributions, statistics & realisations).

DISTRIBUTIONS

<un:Distribution definition="http://dictionary.uncertml.org/distributions/gaussian"> <un:parameters> <un:Parameter definition="http://dictionary.uncertml.org/distributions/gaussian/mean"> <un:value>34.564</un:value> </un:Parameter> <un:Parameter definition="http://dictionary.uncertml.org/distributions/gaussian/variance"> <un:value>67.45</un:value> </un:Parameter> </un:parameters></un:Distribution>

UNCERTMLAn overview

WEAK VS. STRONG

Benefits Generic features

have generic properties – extensible

Drawbacks Validation becomes

less meaningful

Benefits Produces relatively

simple XML features

Drawbacks Not easily extended

– all domain features must be known a priori

Weak-typed Strong-typed

<Distribution definition=“http://uncertml.org/gaussian”> <parameter definition=“http://uncertml.org/mean”>34.2</parameter> <parameter definition=“http://uncertml.org/variance”>12.4</parameter></Distribution>

<GaussianDistribution> <mean>34.2</mean> <variance>12.4</variance></GaussianDistribution>

THE UNCERTML DICTIONARY

Weak-typed designs rely on dictionaries.

Includes definitions of key distributions & statistics.

URIs link to dictionary entry and provide semantics.

Could be written in Semantic Web standards (OWL, RDF etc).

<gml:Dictionary xmlns:gml="http://www.opengis.net/gml" gml:id="DISTRIBUTIONS"> <gml:name>All Probability Distributions</gml:name> <gml:description>Distributions dictionary</gml:description> <gml:dictionaryEntry> <un:DistributionDefinition xmlns:un="http://www.intamap.org/uncertml" gml:id="Gaussian"> <gml:description>Gaussian distribution</gml:description> <gml:name>Gaussian</gml:name> <gml:name>Normal</gml:name> <un:functions> <un:FunctionDefinition gml:id="Gaussian_Cumulative_Distribution_Function"> <gml:description>cumulative distribution function</gml:description> <gml:name>Cumulative Distribution Function</gml:name> <un:mathML> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac>

UNCERTML – DICTIONARY EXAMPLE

SEPARATION OF CONCERNS

Several competing standards already exist addressing the issue of units and location.

Geospatial information not always relevant – Systems biology.

Do what we know – do it well!

UNCERTMLAn applied case study

THE INTAMAP PROJECT

An automatic, interoperable service providing real time interpolation between observations.

EURDEP providing radiological data as a case study.

Provide real time predictions to aid risk management through a Web Processing Service interface.

UNCERTML IN INTAMAP ‘Really clever’ Bayesian

inference: Different sensor errors. Change of support.

Fast & approximate algorithms.

COMPARING PREDICTIONS WITH AND WITHOUT UNCERTML

Without UncertML With UncertML

CONCLUSIONSCurrently no interoperable standard

which fully describes random variables.

UncertML provides an extensible, weak-typed, design that can quantify uncertainty using:Distributions.Statistics.Realisations.

Provide richer information for use in decision support systems.

UNCERTML IN INTAMAP<om:Observation><om:procedure xlink:href="http://www.mydomain.com/sensor_models/temperature"/> <om:resultQuality> <un:Distribution definition="http://dictionary.uncertml.org/distributions/gaussian"> <un:parameters> <un:Parameter definition="http://dictionary.uncertml.org/distributions/gaussian/parameters/mean"> <un:value>0.0</un:value> </un:Parameter> <un:Parameter definition="http://dictionary.uncertml.org/distributions/gaussian/parameters/variance"> <un:value>3.6</un:value> </un:Parameter> </un:parameters> </un:Distribution> </om:resultQuality> <om:observedProperty xlink:href="urn:x-ogc:def:phenomenon:OGC:AirTemperature"/> <om:featureOfInterest> <sa:SamplingPoint> <sa:sampledFeature xlink:href="http://www.mydomain.com/sampling_stations/ws-04231"/> <sa:position> <gml:Point> <gml:pos srsName="urn:x-ogc:def:crs:EPSG:4326"> 52.4773635864 -1.89538836479 </gml:pos> </gml:Point> </sa:position> </sa:SamplingPoint> </om:featureOfInterest> <om:result xsi:type="gml:MeasureType" uom="urn:ogc:def:uom:OGC:degC">19.4</om:result></om:Observation>

<un:DistributionArray> <un:elementType> <un:Distribution definition="http://dictionary.uncertml.org/distributions/gaussian"> <un:parameters> <un:Parameter definition="http://dictionary.uncertml.org/distributions/gaussian/mean"/> <un:Parameter definition="http://dictionary.uncertml.org/distributions/gaussian/variance"/> </un:parameters> </un:Distribution> </un:elementType> <un:elementCount>5</un:elementCount> <swe:encoding> <swe:TextBlock decimalSeparator="." blockSeparator=" " tokenSeparator=","/> </swe:encoding> <swe:values> 35.2,56.75 31.2,65.31 28.2,54.23 35.6,45.21 41.5,85.24 </swe:values></un:DistributionArray>