Predictive modeling re ects the process of using data and statistical or data mining methods for predicting new observations. The predictive models that are created out of this process could be reused in di erent applications in the same sense that open data is reused. Towards this end, a few standards have been proposed in order to enable transfer of predictive models across platforms and applications. In this paper we suggest the need for incorporating predictive models into the Linked Data Web. Towards this end, we propose an RDF Schema vocabulary that will enable the creation of predictive models descriptions adhering to the Linked Data principles. The incorporation of these descriptions into the Linked Data Web could create new potentials beyond cross-platform model reuse. In particular, it will enable (a) easy discovery and reuse of appropriate models at a Web Scale and (b) creation of more accurate models exploiting connections of models to other models, datasets and other resources on the Web.
In the context of quantitative empirical modeling, the term predictive analytics
refers to the building and assessment of a model aimed at making empirical
predictions using data and statistical or data mining methods [
These predictive models can be reused by di erent applications, in the same
way that open data is reused [
In addition, predictive models incorporate knowledge about a domain or a problem area. For example, a model could include variables that e ect economic development. However, usually more than one models can be created about a speci c problem using di erent data and statistical or data mining methods. These models provide fragmented views on a speci c problem. Moreover, these views could be either complementary or controversial. As a result the capability of connecting these di erent views could enhance the understanding of a problem and could facilitate the building of more accurate models.
At the same time, the adoption of the Linked Data principles and technologies
[
In this paper we suggest that the incorporation of predictive models into the Linked Data Web could enable new potentials beyond the reuse of models across di erent platforms. In particular, this could enable the discovery of predictive models at a Web scale in an easy and e ective manner. For example, it will make possible queries such as \On which data mining method the most accurate model that predicts in uenza-like illnesses from Google queries is based on?" or \What predictor variables should a model aiming at predicting unemployment include?". Moreover, in this paper we propose an RDF Schema vocabulary, named the Linked Statistical Models (limo) vocabulary, that will enable the incorporation of descriptions of predictive models into the Linked Data Web and establish links to other resources such as datasets, other models, academic articles and studies.
The remaining of the paper is organized as follows. In section 2 we describe the motivation behind the incorporation of predictive models descriptions into the Linked Data Web. In section 3 we present related work regarding (a) existing endeavors for describing predictive models and (b) widely used RDF vocabularies in the area of statistics. Section 4 presents the Linked Statistical Models (limo) vocabulary. Finally, in section 5 a number of use cases are presented while in section 6 conclusions are drawn along with future work.
Di erent models could present controversial results in the same problem area
and for the same variables depending on the statistical methods and/or the
data that have been employed. For example, Chiricos [
In addition, statistical models that have been developed based on a speci c dataset can indeed be reused in another case. For example, a model developed for predicting sales based on data from Company X could be e ciently reused with data from Company Z. Moreover, a model predicting sales using a speci c data mining method can be reused as a baseline for another model that uses a di erent method.
Publishing descriptions of statistical models on the Web following the Linked Data principles could have the following bene ts: 1. Discovery of variables that a predictive relationship between them have been suggested by an empirical model. For example, it will be possible to discover that X number of models show a predictive relationship between product sales and advertising budget while Z number of models show a negative or no relationship between them. 2. Discovery of all predictor variables that are connected to product sales through successful empirical predictive models. 3. Discovery of statistical or data mining methods that have been used to identify relationships between variables. For example, most of the models that are able to accurately predict product sales from advertising budget have used linear regression methods. 4. Discovery of datasets that have been used to identify predictive relationships between variables. For example, models that show a strong predictive relationship between product sales and advertising budget have employed data from the U.S. in the period between 1975 and 2004. 5. Discovery of a speci c predictive model that shows a relationship between variables based on aspects such as its creator, the a liation of the creator, the journal that the results have been published in, etc. 6. Discovery of new datasets in order to reuse existing models. For example, identi cation of datasets in Europe from the last ten years in order to reuse a predictive model produced with data from the U.S. 7. Discovery of predictive models that could be used as baseline models in building new more accurate predictive models.
These bene ts will be achieved only if a vocabulary to model predictive models as RDF will be speci ed and Linked Data descriptions of predictive models will be published at a wide range. The scoping of this paper focuses on the former. 3
The Predictive Model Markup Language (PMML) is an XML standard that
represents and describes data mining and statistical models, as well as some of
the operations required for cleaning and transforming data prior to modeling
[
This structure presents only top-level elements. PMML is a very rich language that speci es a very big number of both elements and attributes that are related to data setup, data pre-processing and model representation. All these elements aim at enabling model reuse across heterogeneous platforms and environments for all the major statistical and data mining techniques. We should, however, note that the rst version of limo that is presented in this paper does not intend to cover all the details required for importing and executing a predictive model into an actual platform.
In addition, a number of widely used RDF Schema vocabularies are closely
related to statistics. The DDI-RDF vocabulary [
The DDI-RDF contains the disco:aggregation property that indicates that a qb:DataSet was derived by aggregating a record-level dataset. Moreover, the DDI-RDF vocabulary uses the class disco:Variable which provides a de nition of the column in a rectangular data le and thus enables understanding of the content of a dataset. In addition, it de nes the disco:LogicalDataSet class and subclass of dcat:Dataset to provide a description of the content of a data set. disco:LogicalDataSet is associated with disco:DataFile, subclass of dcat:Distribution as well as of dctype:Dataset, that actually represents the physical subsistence of the data set. A disco:LogicalDataset is organized into a set of instances of disco:Variable.
In RDF Data Cube, the qb:DataSet represents the resource of the entire data set, a data set that corresponds to the de ned structure of the RDF Data Cube. The data sets are allowed to be organized in several slices. The structure of qb:DataSet or of a slice of the actual data is de ned by the class qb:DataStructureDefinition. qb:DataStructureDefinition associates to the qb:component property in order to specify the component(s) of the datasets structure. The qb:ComponentProperty is the super class property of the properties that represent dimensions, measures and attributes namely qb:Dimension Property, qb:MeasureProperty and qb:AttributeProperty respectively.
Finally, based on these modeling endeavors a number of open statistical
datasets published by important international organizations such as the OECD,
the World Bank and the IMF have been transformed to Linked Data by third
parties [
In this section we present the RDF Linked Statistical Models (limo) vocabulary that allows for the description of statistical and data mining models in the RDF model and thus enables the incorporation of these models on the Linked Data Web and linking to others resources such as datasets, organizations, people and articles.
In general, predictive analytics comprise predictive models designed for
predicting new (or future) observations or scenarios as well as methods for
evaluating the predictive power of a model [
The vocabulary's main classes are depicted in Fig. 1. Classes and properties from existing widely used vocabularies were reused whenever possible. { limo:Model is the actual predictive model that is described by the vocabulary. The model has the following attributes: { dct:title which is a name given to describe the model. { dct:description for a descriptive comment about the model and its goals. { dct:issued which de nes the actual data that the model has been created. { limo:modelType which describe the main categories of models that can be developed, namely classi cation, regression, clustering and dimensionReduction. { limo:spatial is an attribute that describe the spatial dimension of the model. The spatial dimension of the model is derived from the actual data that have been employed. For example, a model could have limo:spatial U.S. in the case the data used for the development of the model comes from the U.S. { limo:temporal is an attribute that describe the time period that the model covers. The time period of the model re ects the period that is described in the actual data that have been used for the development of the model. limo:Model is connected through limo:data property to a multi-dimensional data set i.e. a qb:DataSet. This dataset contains the actual data that have been used for the development of the model. As a result, the temporal and spatial dimension of the model could be also extracted from this dataset. In predictive analytics we have three di erent types of data, namely evaluation, validation and training data. So, limo includes three di erent sub-properties of the limo:data property, one for each of these three types of data. limo:Model is also connected through limo:rawData property to a dctype: Dataset. This dataset includes the raw data that have been used in the process of building the model. For example, this dataset could be a dump of raw tweets or a dcat:Dataset which thereafter was analyzed in order to produce the actual data employed be the model.
Moreover, the limo:Model can be connected to a di erent limo:Model through the limo:baseline property which explicitly denotes that the predictive power of a model has been evaluated against the power of another model. The limo:Model can be also published in a scienti c article or report. Hence we have included the limo:publishedIn property to express this relationship. Finally, limo:Model is connected to a foaf:Agent through the dct:creator property. This property denotes the person or organization that actually builds the model. { limo:Variable represents the variables that are included in the predictive model. The Variable class includes the following attributes { The dct:title denotes the actual name of the variable. { The dct:description enables the inclusion of a small text in order to describe what the variable is about. { The limo:variableType attributes denotes whether the variable is continuous, categorial or ordinal. { The limo:usageType denotes whether the variable is the response of the model or one of the predictors.
In addition, limo:Variable is categorized using the limo:theme property which connects the Variable to a skos:Concept { limo:Method describes the statistical or data mining method used for creating the model. We assume that this class uses a set of prede ned concepts such as linear regression, logistic regression, markov models, support vector machine, random forests, neural networks etc. As a result, we assume that limo:Method is subclass of skos:Concept. { limo:Power describes the predictive power of the model. The predictive power has the following attributes: { limo:evaluationMethod is used to infer the predictive power of a model. The evaluation methods include out-of-sample evaluation with statistics such as Predicted Residual Sums of Squares, Root Mean Square Error or crossvalidation techniques.
{ limo:outcome is the actual value that the evaluation method produces. { limo:File describes a le that can be imported in a particular platform such as R or SAS and execute the model. This could also be a PMML-XML le.
We should note that in this preliminary version of the vocabulary the execution of the model is possible through a PMML XML le. In the next version we aim at providing a more detailed description of the model in order to enable the execution of a model through its limo description. Full documentation of the limo vocabulary is available online4. 5
In this section we present how limo vocabulary can be used in order (a) to describe a predictive model and (b) to enable the discovery of predictive models that address some requirements.
Below we present the limo description of the predictive model developed by
Ginsberg et al. and presented in [
qb:DataSet limo:evaluationData limo:validationData limo:trainingData limo:baseline limo:publishedIn limo:file dct:BibliographicResource
limo:File limo:accessURL limo:power
limo:data dctype:Dataset limo:rawData
Fig. 1. The Linked Statistical Models vocabulary a linear regression method as well as data from Google and the US Centers for Disease Control and Prevention. The data is about nine regions of the United States between 2003 and 2008. The model was assessed using cross validation against out-of-sample data partitions and they obtained a mean correlation of 0.97.
Description of the predictive model presented in [
dct:resource <http://www.cdc.gov/flu/weekly>.
In addition, limo will enable the performance of queries across distributed description of predictive models. For example below we present a query answering the question \How many models exist that show relationship between the percentage of in uenza-related physician visits and the probability that a random search query submitted from a region is in uenza-related?".
A query for identifying models that predict in uenza-like illnesses from search query data
} } UNION { ?model limo:variable ?variable1;
limo:variable ?variable2. ?variable1 limo:usageType eg:response;
limo:theme eg:ILIphysvisits; ?variable2 limo:usageType eg:predictor;
limo:theme eg:ILIrandquery; ?model limo:variable ?variable1;
limo:variable ?variable2. ?variable1 limo:usageType eg:predictor;
limo:theme eg: LIphysvisits. ?variable2 limo:usageType eg:response;
limo:theme eg: ILIrandquery.
Moreover, a query based on limo could unveil the variables that are predictors of in uenza-related physician visits through empirical model(s) constructed by data regarding the U.S. The identi cation of these variables could enhance the process of building predictive model for in uenza illnesses.
A query for identifying predictors of inluenza-like illnesses
WHERE { } ?model limo:variable ?variable1. limo:variable ?variable2.
limo:spatial ?sp1. ?variable1 limo:usageType eg:predictor. ?variable2 limo:usageType eg:response; limo:theme eg:ILIphysvisits. ?sp1 rdf:type dbpedia:United_States.
Predictive analytics refer to the process of building a model that enables the prediction of new observations using data and statistical or data mining methods. Predictive models are very important in businesses, academia and governments as they can predict values such as sales and identify patterns regarding e.g. pro table customers or the behavior of citizens. These models can be indeed reused across platforms and in di erent cases. Although, standards for transferring models across di erent platforms have been proposed, at the moment it is di cult to discover an appropriate model for a task at hand at a Web scale.
In this paper we suggested that descriptions of predictive models should be incorporated into the Linked Data Web and we proposed an RDF Scheme vocabulary towards this end. We described the main classes of the vocabulary and we presented an example of how the vocabulary can be used in order to describe a predictive model. We also demonstrated how the vocabulary can be used in order to facilitate the discovery of predictive models.
We believe that the adoption of the vocabulary could create new potentials beyond cross-platforms reuse of models. In particular, the vocabulary will enable (a) easy discovery and reuse of appropriate models at a Web Scale and (b) creation of more accurate models exploiting connections of models to other models, datasets and other resources on the Web.
Future work includes further evaluation of the vocabulary by describing a larger number of predictive models and by incorporating a linked data set into the linked data cloud. This will enable the execution of more complex queries and the evaluation of the vocabulary in real world settings. In addition, the possibility of extending limo with execution capabilities will be considered. This includes enriching limo with classes and attributes that will allow for importing RDF data into popular open platforms such as R and executing the actual model.
The work presented in this paper was partially carried out in the course of the Linked2Safety 5 project, which is funded by the European Commission within the 7th Framework Programme under grand agreement No. 288328.