API proposal for applicability domain estimation

Applicability domain in OpenTox framework:

• An applicability domain procedure is an OpenTox Algorithm.
• An applicability domain "model" is created posting a dataset URI to an applicability domain algorithm URI.  This creates ot:Model with type ota:ApplicabilityDomain and returns a "AD-model" uri.
• Alternatively, for AD, embedded in a predictive model, just declare additional rdf:type of the model to be ota:ApplicabilityDomain
  
• An applicability domain estimation is done by POSTing a dataset to the "AD-model" uri.  This generates another dataset with an extra feature telling whether the corresponding compound belongs to the applicability domain (or in fuzzy terms, how much does it belong to that set).
• For models with embedded AD, on POST of a dataset to the model , both prediction results and AD estimates are generated.
  
• All models provides the estimation results as specified below.
  

Applicability domain RDF representation:

A predictive model can be assigned external or embedded applicability domain

• In case of AD external to the model:

@prefix ot:      <http://www.opentox.org/api/1.1#> .
@prefix ota:     <http://www.opentox.org/algorithmTypes.owl#> .

</model/mlr-model> ot:hasDomain </model/leverage-ad-model>.

</model/mlr-model> rdf:type ot:Model.
</model/mlr-model> ot:algorithm </algorithm/mlr>.
</algorithm/mlr> rdf:type ot:Algorithm.
</algorithm/mlr> rdf:type ota:Regression.

</model/leverage-ad-model> rdf:type ot:Model.
</model/leverage-ad-model> ot:algorithm </algorithm/leverage>.
</algorithm/leverage> rdf:type ot:Algorithm.
</algorithm/leverage> rdf:type ota:ApplicabilityDomain.

• In case of AD embedded with the model

@prefix ot:      <http://www.opentox.org/api/1.1#> .
@prefix ota:     <http://www.opentox.org/algorithmTypes.owl#> .

<lazar-model> ot:hasDomain <lazar-model>.

<lazar-model> rdf:type ot:Model.
<lazar-model> ot:algorithm </algorithm/lazar>.

</algorithm/lazar> rdf:type ot:Algorithm.

</algorithm/lazar> rdf:type ota:ApplicabilityDomain.
</algorithm/lazar> rdf:type ota:LazyLearning.

Results form applicability domain estimation

• by analogy of ot:predictedVariables, used to specify features, where prediction results are stored, one can specify which features hold the result of AD estimation (suggestion for better property names instead of ot:adMembership and ot:adMetric are welcome !)
  

@prefix ot:      <http://www.opentox.org/api/1.1#> .

//the estimated value, e.g. leverage
ot:Model ot:adMetric ot:Feature.

//the desision for AD membership, based on the estimated value - e.g. "in-domain" if leverage > threshold
//have to agree on the value type - boolean, numeric, string, nominal ?
ot:Model ot:adMembership ot:Feature.

and subsequently use the same ot:dataEntry and ot:FeatureValue RDF constructions , used elsewhere to specify property values, to specify AD results as well:

@prefix ot:      <http://www.opentox.org/api/1.1#> .
@prefix dc:      <http://purl.org/dc/elements/1.1/> .
@prefix :        <http://ambit.uni-plovdiv.bg:8080/ambit2/> .
@prefix ota:     <http://www.opentox.org/algorithmTypes.owl#> .
@prefix rdfs:    <http://www.w3.org/2000/01/rdf-schema#> .
@prefix owl:     <http://www.w3.org/2002/07/owl#> .
@prefix xsd:     <http://www.w3.org/2001/XMLSchema#> .
@prefix ac:      <http://ambit.uni-plovdiv.bg:8080/ambit2/compound/> .
@prefix ad:      <http://ambit.uni-plovdiv.bg:8080/ambit2/dataset/> .
@prefix rdf:     <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix af:      <http://ambit.uni-plovdiv.bg:8080/ambit2/feature/> .


ad:1  a       ot:Dataset ;
      ot:dataEntry
              [ a       ot:DataEntry ;
                ot:compound ac:1 ;
                ot:values
                        [ a       ot:FeatureValue ;
                          ot:feature af:1 ;
                          ot:value "3.14"^^xsd:double
                        ]

                ot:values
                        [ a       ot:FeatureValue ;
                          ot:feature af:9999 ;
                          ot:value "0.0"^^xsd:double
                        ]
              ] .

af:1
      a       ot:Feature , ot:NumericFeature ;
      dc:title "MLR-prediction" ;
      ot:hasSource <http://opentox.ntua.gr/model/mlr> ;
      ot:units "" .


af:9999
      a       ot:Feature , ot:NumericFeature ;
      dc:title "AD-leverage" ;
      ot:hasSource <http://opentox.ntua.gr/model/leverage-ad> ;
      ot:units "" .


ac:1
      a       ot:Compound ;

ot:NumericFeature
      a       owl:Class ;
      rdfs:subClassOf ot:Feature .

ot:DataEntry
      a       owl:Class .

ot:hasSource
      a       owl:ObjectProperty .

ot:units
      a       owl:DatatypeProperty .

ot:values
      a       owl:ObjectProperty .

ot:compound
      a       owl:ObjectProperty .

dc:title
      a       owl:AnnotationProperty .

ot:feature
      a       owl:ObjectProperty .

ot:Dataset
      a       owl:Class .

dc:description
      a       owl:AnnotationProperty .

ot:dataEntry
      a       owl:ObjectProperty .

ot:Compound
      a       owl:Class .

dc:identifier
      a       owl:AnnotationProperty .

ot:FeatureValue
      a       owl:Class .

ot:Feature
      a       owl:Class .

dc:type
      a       owl:AnnotationProperty .

ot:value
      a       owl:DatatypeProperty .

There is no difference in representation of AD results, if AD is embedded in the model itself, besides that ot:hasSource for features , representing predicted values and AD estimation, point to the same ot:Model object

ad:1  a       ot:Dataset ;
      ot:dataEntry
              [ a       ot:DataEntry ;
                ot:compound ac:1 ;
               ot:values
                        [ a       ot:FeatureValue ;
                          ot:feature af:lazar_prediction ;
                          ot:value "1.0"^^xsd:double
                        ]
                ot:values
                        [ a       ot:FeatureValue ;
                          ot:feature af:10000 ;
                          ot:value "0.666"^^xsd:double
                        ]
              ] .

af:10000
      a       ot:Feature , ot:NumericFeature ;
      dc:title "AD-lazar" ;
      ot:hasSource <http://in-silico.ch/model/lazar> ;
      ot:units "" .


af:lazar_prediction
      a       ot:Feature , ot:NumericFeature ;
      dc:title "prediction-lazar" ;
      ot:hasSource <http://in-silico.ch/model/lazar> ;
      ot:units "".

ac:1
      a       ot:Compound ;