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|pdfUrl=https://ceur-ws.org/Vol-1549/article-09.pdf
|volume=Vol-1549
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https://ceur-ws.org/Vol-1549/article-09.pdf
Towards a Vocabulary for Incorporating
Predictive Models into the Linked Data Web
Evangelos Kalampokis1,2 , Areti Karamanou1,2 , Efthimios Tambouris1,2 , and
Konstantinos Tarabanis1,2
1
Information Systems Lab, University of Macedonia,
Egnatia 156, 54006 Thessaloniki, Greece
2
Informatics and Telematics Institute, Centre for Research & Technology - Hellas
6th km Xarilaou - Thermi, 57001, Thessaloniki
{ekal,akarm,tambouris,kat}@uom.gr
Abstract. Predictive modeling reflects 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
different 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.
Keywords: Linked data, statistical data, predictive analytics, vocabu-
lary, RDF, predictive model, interoperability
1 Introduction
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 [1]. In general, the
goal of predictive models is to predict the output value (Y) for new observations
given their input values (X). The inputs are often called the predictors, and more
classically the independent variables while the outputs are called the response,
or classically the dependent variables. Examples of predictive models consider
the prediction of stock market volatility from Yahoo! Finance message board
[2], movies success from weblog content [3], influenza-like illnesses from Google
search queries [4], product sales from Amazon reviews [5] and levels of rainfall
from Twitter posts [6].
2 A Vocabulary for Predictive Models on the Linked Data Web
These predictive models can be reused by different applications, in the same
way that open data is reused [7, 8]. Towards this end, standardization activities
such as the Predictive Model Markup Language (PMML)3 has been suggested.
This XML–based language enables importing and exporting developed models
as components in other processes and systems using XML files. However, the
discovery of an appropriate model for a task at hand is at the moment a time
consuming activity that requires a lot of manual effort involving searching in
scientific articles, contacting researchers or professionals and exchanging files.
In addition, predictive models incorporate knowledge about a domain or a
problem area. For example, a model could include variables that effect economic
development. However, usually more than one models can be created about a
specific problem using different data and statistical or data mining methods.
These models provide fragmented views on a specific problem. Moreover, these
views could be either complementary or controversial. As a result the capability
of connecting these different 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
[9] has promised to enhance the analysis of statistical data at a Web scale.
For example, Linked Data could facilitate performing data analytics on top of
combined statistical datasets that were previously closed in disparate sources
and can now be linked in order to provide unexpected and unexplored insights
into different domains and problem areas [10]. Moreover, linking statistical data
to the Linked Data Web could enable the enrichment of a particular dataset
and thus the extraction of interesting and previously hidden insights related to
particular events [11].
In this paper we suggest that the incorporation of predictive models into
the Linked Data Web could enable new potentials beyond the reuse of mod-
els across different platforms. In particular, this could enable the discovery of
predictive models at a Web scale in an easy and effective manner. For exam-
ple, it will make possible queries such as “On which data mining method the
most accurate model that predicts influenza-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.
3
http://www.dmg.org
A Vocabulary for Predictive Models on the Linked Data Web 3
2 Motivation
Different 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 [12] reviewed 68 studies
about the relationship between crime and the unemployment rate and he found
that only less than half of these studies have found positive significant effects of
the unemployment on crime rates. In addition, Kalampokis et al. [13] reviewed
52 empirical predictive models that employ predictors related to Social Media.
They identified that the predictive power of a model is directly related to the
predictors, the statistical method, the datasets and the evaluation method that
have been selected. Thus, in order to better understand a problem we need to be
able to discover and analyze various models that share common characteristics.
In addition, statistical models that have been developed based on a specific
dataset can indeed be reused in another case. For example, a model developed
for predicting sales based on data from Company X could be efficiently reused
with data from Company Z. Moreover, a model predicting sales using a specific
data mining method can be reused as a baseline for another model that uses a
different method.
Publishing descriptions of statistical models on the Web following the Linked
Data principles could have the following benefits:
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 iden-
tify 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 rela-
tionship between product sales and advertising budget have employed data
from the U.S. in the period between 1975 and 2004.
5. Discovery of a specific predictive model that shows a relationship between
variables based on aspects such as its creator, the affiliation 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,
identification 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.
4 A Vocabulary for Predictive Models on the Linked Data Web
These benefits will be achieved only if a vocabulary to model predictive
models as RDF will be specified and Linked Data descriptions of predictive
models will be published at a wide range. The scoping of this paper focuses on
the former.
3 Related Work
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
[14]. PMML aims to provide enough infrastructure for an application to be able
to produce a model and another application to consume by reading the PMML
XML data file [15]. PMML has the following general structure:
– The Header contains information about the application generated the model
including a time stamp.
– The Mining Build Task contains vendor specific information about how the
model was built.
– The Data Dictionary contains details about the variables, called Data Fields
that participate in the model. These can be though of representing the actual
data used to develop the model including information such as the name, the
type of data (e.g. string, numeric) and how it is used (e.g. is it a continuous
numeric value, a categorical value, etc.).
– The Transformation Dictionary describes how to manipulate the data fields
from the data dictionary into variables that exist within the PMML defini-
tion. This includes normalization, discretization, value mapping etc.
– The Model that contains model-specific features according to the model
types (e.g. association rules, clustering, general regression, support vector
machines, and neural networks). For instance, the NeuralNetwork element
includes the activationFunction attribute that specifies the activation func-
tion to be used by the network neurons when processing incoming data.
Furthermore, it contains elements that are common to all model types such
as Outputs that define the different types of results (e.g. predictedValue,
standardError, probability, residual ) that can be generated by a model and
Mining Schema that defines what to do in case any of the data fields de-
fined in the DataDictionary element are missing or contain invalid or outlier
values.
This structure presents only top-level elements. PMML is a very rich language
that specifies 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 first 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.
A Vocabulary for Predictive Models on the Linked Data Web 5
In addition, a number of widely used RDF Schema vocabularies are closely
related to statistics. The DDI-RDF vocabulary [16] focuses on raw record-level
datasets and describes their structure, while the RDF Data Cube vocabulary
[17] aims at multidimensional aggregated data and provides for the description
of both the structure and the actual data of a dataset.
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 defini-
tion of the column in a rectangular data file and thus enables understanding
of the content of a dataset. In addition, it defines 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 defined 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 defined 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 prop-
erties 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 [18, 19]. Towards this end, a number of tools have been developed. For
example, Capadisli et al. [18] created a tool for transforming statistical data
from SDMX-ML format to Linked Data while Salas et al. [20] from CSV and
OLAP databases.
4 The limo Vocabulary
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 pre-
dicting new (or future) observations or scenarios as well as methods for evalu-
ating the predictive power of a model [21]. The outcome value for a new set of
observation could be continuous (or quantitative) or categorical (or qualitative).
In the former case the problem is ofter referred to as a regression problem while
in the latter a classification problem. Predictive power refers to an empirical
6 A Vocabulary for Predictive Models on the Linked Data Web
models ability to predict new observations accurately. In contrast, explanatory
power refers to the strength of association indicated by a statistical model.The
predictive power of a model should be tasted based on out-of-sample data (e.g.
cross-validation or a holdout sample) and with adequate predictive measures
(e.g. RMSE, MAPE, PRESS etc.). A popular method to obtain out-of-sample
data is to initially partition the data randomly, using one part (the training set)
to fit the empirical model, and the other (the holdout set) to assess the model’s
predictive accuracy.
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 vocabu-
lary. 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 defines the actual data that the model has been created.
– limo:modelType which describe the main categories of models that can
be developed, namely classification, regression, clustering and dimensionRe-
duction.
– 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 reflects 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 different types of data, namely evaluation,
validation and training data. So, limo includes three different 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 different 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 scientific article or report. Hence
we have included the limo:publishedIn property to express this relation-
ship.
A Vocabulary for Predictive Models on the Linked Data Web 7
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 de-
scribe what the variable is about.
– The limo:variableType attributes denotes whether the variable is contin-
uous, 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 cre-
ating the model. We assume that this class uses a set of predefined 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 cross-
validation techniques.
– limo:outcome is the actual value that the evaluation method produces.
– limo:File describes a file that can be imported in a particular platform
such as R or SAS and execute the model. This could also be a PMML-XML
file.
We should note that in this preliminary version of the vocabulary the exe-
cution of the model is possible through a PMML XML file. 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 Using limo
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 [4]. This model aims at predicting influenza-
like illness (ILI) physician visits from ILI-related queries. The models employs
4
http://purl.org/limo-ontology/limo
8 A Vocabulary for Predictive Models on the Linked Data Web
dctype:Dataset
limo:PredictivePower qb:DataSet
limo:evaluationMethod
limo:outcome
limo:rawData
limo:data limo:evaluationData
limo:power limo:validationData
foaf:Agent limo:trainingData
dct:creator
limo:Model
dct:title
dct:description limo:baseline
dct:issued
limo:modelType
limo:spatial
limo:temporal
limo:publishedIn
limo:method dct:BibliographicResource
limo:variable
limo:Method limo:file
limo:Variable
dct:title
dct:description
imo:variableType limo:File
limo:usageType limo:accessURL
skos:Concept
limo:theme
skos:Concept
Fig. 1. The Linked Statistical Models vocabulary
A Vocabulary for Predictive Models on the Linked Data Web 9
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 [4] with limo
eg:DDCILImodel a limo:Model;
dct:title "CDC-ILI model"@en;
limo:spatial [rdf:type dbpedia:United_States];
limo:temporal
[a dc:terms PeriodOfTime;
limo:startDate "2003-09-28"^^xsd:date;
limo:endDate "2008-05-11"^^xsd:date;];
limo:modelType eg:regression;
limo:variable eg:resp;
limo:variable eg:pred;
limo:method eg:linearregression;
limo:power eg:CDCILIpower;
limo:file eg:CDCILIfile;
limo:rawData eg:CDCILIdataset;
limo:evaluationData eg:CDCILIevaluationdata;
limo:validationData eg:CDCILIvalidationdata;
limo:trainingData eg:CDCILItrainingdata;
dct:creator eg:ginsberg, eg:mohebbi, eg:patel, eg:brammer,
eg:smolinski, eg:brilliant;
eg:resp a limo:Variable;
limo:variableType eg:continuous;
dct:description "Percentage of physician visits in which a
patient presents with influenza-like symptoms in a region"@en;
limo:usageType eg:response;
limo:theme eg:ILIphysvisits.
eg:pred a limo:Variable;
limo:variableType eg:continuous;
dct:description "Probability that a random search query
submitted from a region is ILI-related"@en;
limo:usageType eg:predictor;
limo:theme eg:ILIrandquery.
eg:CDCILIpower a limo:Power;
limo:evaluationMethod eg:crossvalidation;
limo:outcome 0.97.
eg:CDCILIdataset a dctype:DataSet;
dct:resource .
In addition, limo will enable the performance of queries across distributed de-
scription of predictive models. For example below we present a query answering
10 A Vocabulary for Predictive Models on the Linked Data Web
the question “How many models exist that show relationship between the per-
centage of influenza-related physician visits and the probability that a random
search query submitted from a region is influenza-related?”.
A query for identifying models that predict influenza-like illnesses from search
query data
SELECT (count( ?model ) as ?nmodels)
WHERE {
{
?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;
} UNION
{
?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 influenza-related physician visits through empirical model(s) constructed by
data regarding the U.S. The identification of these variables could enhance the
process of building predictive model for influenza illnesses.
A query for identifying predictors of inluenza-like illnesses
SELECT ?variable
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.
}
A Vocabulary for Predictive Models on the Linked Data Web 11
6 Conclusions
Predictive analytics refer to the process of building a model that enables the pre-
diction 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.
profitable customers or the behavior of citizens. These models can be indeed
reused across platforms and in different cases. Although, standards for transfer-
ring models across different platforms have been proposed, at the moment it is
difficult 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) cre-
ation 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.
Acknowledgments
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.
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