Machine learning represents a pragmatic breakthrough in making predictions by nding complex structures and patterns in large volumes of data. Open Statistical Data (OSD), which are highly structured and generally of high quality, can be used in advanced decision making scenarios that involve machine learning analysis. Linked data technologies facilitate the discovery, retrieval, and combination of data on the Web. They enable this way the wide exploitation of OSD in machine learning. A challenge in such analyses is to specify the criteria for selecting the proper datasets to combine and construct a predictive model. This paper presents a case study that aims at creating a model to predict house sales prices in ne grained geographical areas in Scotland using a large variety of Linked Open Statistical Data (LOSD) from the Scottish o cial statistics portal. To this end, we present the machine learning analysis steps that can be enhanced using LOSD and we de ne a set of compatibility criteria. A software tool is also presented as a proof of concept for facilitating the exploitation of LOSD in machine learning. The case study proves the importance of discovering and combining compatible datasets when implementing machine learning scenarios for decision-making.
Opening up data for others to reuse is a priority in many countries around the
globe. Although the global annual economic potential of open data is estimated
to $3 trillion [
A promising path to overcome open data barriers is to focus on numerical
data and, more speci cally, statistics [
However, OSD are barely used in advanced decision-making scenarios that
involve machine learning analysis. Machine learning represents a pragmatic
breakthrough in making predictions by nding complex structures and patterns in
large volumes of data. Recent examples indicating the potential of applying
machine learning in statistical data to support decision making include the identi
cation of important factors related to bicycle crashes [
This di culty of using statistical data in advanced machine learning scenarios
can be explained, among others, by the fragmented environment of OSD [
Linked data technologies facilitate discovering, retrieving and combining of
data on the Web by semantically annotating data, creating links between them
and enabling their access using the query language SPARQL. Linked data have
been recently become a W3C standard [
The large volume and variety of datasets provided by LOSD portals are necessary in sophisticated machine learning scenarios in order to create predictive models. A challenge in such scenarios is to specify the criteria that should be considered when selecting datasets to use in order to solve a speci c problem.
The aim of this paper is to present a case study that combines LOSD in order to perform machine learning analysis and support advanced decision-making. Towards this end, we rst specify the criteria that de ne which datasets can be used to solve a problem using machine learning. The datasets of our case study are selected based on these criteria. We also present the Compatible LOSD Selection tool, a proof of concept of the case study that facilitates the selection of datasets that will be combined for machine learning analysis.
The rest of the paper is organised as follows: Section 2 presents the method of this paper. Section 3 de nes the compatibility criteria. Section 4 presents the case study and its results. Section 5 presents the Compatible LOSD Selection tool. Finally, Section 6 concludes and discusses the results.
The method used in the case study includes four steps:
1. Problem de nition. The problem de nition step enables users to de ne the
problem they are interested to solve using machine learning analysis. To this
end, the response variable of the predictive model is de ned (including
geographical boundaries, time constraints, units of measure etc.). This requires
exploring the metadata of available datasets. Moreover, the type of the
problem is speci ed (e.g. regression, classi cation etc.). For example, a problem
could be to predict the 2012 house prices in the 2001 data zones of Scotland.
2. Data selection. The data selection step selects the datasets that will be
combined with the response variable and contribute towards solving the problem
de ned in the previous step. The selection of the datasets uses ve structural
criteria based on the granularity of the geographical dimension, the temporal
dimension, the unit of the measure, the type of the measure and additional
dimensions.
3. Feature extraction. This step extracts from the datasets selected in the
previous step numerous features aka predictors. Features are extracted from the
combination of di erent dimensions and measures in one or more datasets.
Dimensions determine and explain a feature. For example, an
unemployment dataset with four dimensions i.e. age group (15-25, 25-54, 55-64), type
of unemployment (cyclical, frictional, structural), measure type (count,
ratio), reference period (2001-Q1, ..., 2016-Q4) could result in 3 x 3 x 2 x 64
=1152 features.
4. Feature selection and model creation. The feature selection step selects among
all extracted features the ones that will be used to construct the predictive
model. Those are features that are signi cantly correlated to the response
variable. Features considered as redundant or irrelevant are ignored. Machine
learning methods to select features include (Least Absolute Shrinkage and
Selection Operator) Lasso[
LOSD contribute in the second step of the methodology by facilitating the selection of datasets that can be combined with the response variable in order to construct the predictive model. The next Section speci es the criteria to consider in order to select compatible LOSD that can contribute in a predictive model as a response variable or as a feature.
Combining statistical datasets for machine learning
analysis
In general, statistical data are aggregated data that describe a measured fact (e.g.
house prices) in speci c geographical points (e.g. a country, city or building) and
in a speci c period of time (e.g. a year, month, week). In this case, statistical
data are compared to a data cube, where each cell contains a measure or a set
of measures, and thus we can refer to statistical data as data cubes or just cubes
[
The second step of our methodology requires selecting the slices of statistical datasets that will contribute as the response variable (also called Y) and also as the features (also called Xs) of the de ned problem based on:
2. The temporal dimension. 3. The unit of the measure. 4. The type of the measure. 5. Additional dimensions.
We specify the above criteria separately for the response variable and the features. In particular, the selection of the slice that will be used for the response variable is based on: 1. The granularity of the geographical dimension. Commonly the de ned problem focuses on geographical points with a speci c granularity level (e.g. to predict the house prices in the 2001 data zones of Scotland). As a result the slice selected for the response variable should use this speci c granularity level. This will be the open dimension of the slice. 2. The temporal dimension. The de ned problem focuses on a speci c period of time (e.g. to predict the 2012 house prices in the 2001 data zones of Scotland). As a result the slice selected for the response variable should have the time dimension xed to the selected period of time. 3. The unit of the measure. Datasets usually use a unit to describe their measure. Common units of measures are ratio and count. Depending on the problem slices using ratio or count should be selected. If the selected dataset includes more than one units of measure the unit dimension should be xed to the preferred unit of measure. 4. The type of the measure. The measure of a statistical dataset may be categorical or continuous. Continuous measures contain numbers with in nite number of values between any two values. Categorical measures contain a nite number of categories or distinct groups. The nature of the de ned problem will specify the type of the measure to be selected for the slice of the response variable. 5. Additional dimensions. Additional dimensions in the selected slice are desirable (but also optional) as they increase the number of extracted features that could be used in the construction of more reliable predictive models. A common additional dimension is, for example, the gender. Additional dimensions should be also xed to a speci c value.
In addition the selection of the slices for the features is based on: 1. The granularity of the geographical dimension. The slices selected for the X variables of the predictive model should have the same granularity level with the slice of Y. As a result, only datasets that have the same granularity level in the geographical dimension with the Y variable should be selected. 2. The temporal dimension. Machine learning usually aims to predict a speci c phenomenon based on historical data. As a result slices selected for the X variables should refer to the same or past years related to the Y variable. 3. The unit of the measure. Slices using ratio are preferably selected over count because ratio values are normalized. However, slices with count measures can be also selected provided that they will be combined with other count measures in the next step of the methodology (namely feature extraction) in order to construct new ratio variables. For example, one could select a slice counting the number of births and also a slice counting the number of deaths from the data portal of Scotland in order to create in the feature selection step the ratio `number of births/number of deaths'. 4. The type of the measure. In a predictive model it is not mandatory for the Y and X variables to have the same type. As a result, when the Y variable is categorical the Data selection step can select slices with either categorical or continuous measures for the features and vice versa. 5. Additional dimensions. The selected slice can also have additional dimensions (e.g. the gender) with same or di erent values related to the respective dimension of Y. 4
Case Study: Predicting the House Prices in Scotland The case study presented in this paper uses datasets from the o cial statistics data portal of Scotland i.e. http://statistics.gov.scot that was launched in August 2016. At the time of writing the portal provides access to 220 statistical datasets about Scotland. The datasets can be viewed in variable formats including tables, maps and charts or downloaded formats like CSV or N-triples formats. The datasets can be browsed by theme (e.g. Labour Force, Environment, Transport etc.) or by the organisation that published the dataset (e.g. Scottish government, SEPA or Transport Scotland).
Scottish o cial statistics are also provided in Linked Data format using the W3C's RDF Data Cube Vocabulary3 which allows modelling statistical data as data cubes. In particular, each dataset in the portal is modelled as a data
cube. Each data cube provides multiple ancillary dimensions in complement of the indicator which is the measure of the data cube. The two most common dimensions used to describe the datasets are the geographical dimension called Reference area and the temporal dimension called Reference Period. The geographical dimension of the datasets is based on a hierarchy of administrative or consensus-based areas covering from Scottish data zones to electoral awards and countries. Granularity refers to the levels of depth of the reference area dimension of each dataset. Some examples of these levels include country, council areas, electoral wards, and data zones. For example, the house sales dataset4 describes the number of Residential property transactions recorded in di erent geographical levels of Scotland (e.g. Countries, Electoral Wards, 2001 Data zones and others) in di erent reference periods (1993-2017). Other commonly used dimensions include the gender and age group of the population. Problem de nition The objective of the case study presented in this paper is to predict the 2012 mean house prices in the 2001 data zones of Scotland. This is a description of the response variable of our problem.
2001 Data zones were introduced in 2004 and are the smallest geographical granularity level in Scotland. They have populations between 500 and 1,000 household residents. Selecting 2001 data zones for our response variable results in a great number of observations that help to avoid the curse of highdimensionality (i.e. the state of having less observations than features), create a more robust model, and predict prices for a speci c district or neighbourhood.
Regarding the machine learning method used, regression analysis Lasso method is selected to solve the above described problem. Lasso yields sparse models i.e. models that involve only a subset of the variables.
Data selection After the de nition of our problem we rst search for datasets in the Scottish data portal that can contribute as the response variable of our problem. The slice selected for the response variable comes from the dataset House prices of the Scottish portal5 with the temporal dimension xed to 2012, the measure type xed to mean, and the values of the reference area dimension coming from the 2001 data zones in Scotland.
We then search for datasets that can contribute as features. The selected datasets should be compatible with the response variable. For this reason we search in the Scottish data portal for datasets based on the compatibility criteria described in the previous section. In particular, we search for datasets that: 1. The granularity level in their geographical dimension is Scottish 2001 data zones 2. Their temporal dimension refers to a year in the range 2009-2012 4 http://statistics.gov.scot/resource?uri=http%3A%2F%2Fstatistics.gov.
scot%2Fdata%2Fhouse-sales 5 http://statistics.gov.scot/resource?uri=http%3A%2F%2Fstatistics.gov. scot%2Fdata%2Fhouse-sales-prices
4. Have a continuous or categorical measure 5. (Optionally) have additional dimensions
It should be noted that in this case study we only searched for datasets with ratio unit of measure. However, as also described in section 3, count datasets could also be selected provided that they will be transformed in the next step to ratio values.
In addition, some datasets may be truly correlated with the response variable of our case study i.e. the house sales prices and should be excluded. For example, the Council Tax Bands dataset provides the rate of houses that belong to a speci c council tax band in each Scottish data zone. This measure is however actually derived from the price of houses and for this reason we shouldn't include it in our case study. In reality Council tax bands is a discrete measure, which means it aggregates the number of houses according to their value.
The exploration of the Scottish data portal for datasets that satisfy the above criteria results in the selection of 21 compatible datasets.
Feature extraction In this step we extract multiple features from each selected compatible dataset. In our case study each feature is extracted by only one dataset. For instance, the dimensions of the \Age of First Time Mothers" dataset which describes the rate of rst time mothers include reference period and age. For the age dimension three values are used: (1) 19 and under, (2) item 35 and over, and (3) All. If we also consider that we have selected 4 reference periods for our datasets (i.e. 2009, 2010, 2011 and 2012), the nal number of features that can be extracted from this dataset is calculated as:
2 (the two values of the age dimension - \All" is not included) x 1 (the number of the di erent unit types) x 4 (number of reference periods) = 8 features.
The same applies to the rest of the selected datasets in order to extract all features. The feature extraction step results in 450 features.
Feature selection and model creation In order to eliminate insigni cant features we use the regression analysis method called Lasso. The Lasso implementation was made using the glmnet library6. Lasso keeps only the important features (i.e. features which add value to our estimations) and removes the rest of them. A reduced number of features facilitates the interpretation of the results.
In our case study Lasso results in 34 features coming from 10 datasets. The initial number of features (i.e. 450) is hence signi cantly reduced (by more than 92%). The 10 datasets selected are:
6 https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html 3. Breastfeeding 4. Disability Living Allowance 5. Dwellings by Number of Rooms 6. Employment and Support Allowance 7. Hospital Admissions 8. Household Estimates 9. Income And Poverty Modelled Estimates 10. Job Seeker's Allowance Claimants
Table 1 presents the detailed results of the application of the Lasso analysis method. We can see that there is no signi cant change between the Lasso lowest RMSE and the Lasso one standard error.
Lasso uses the cross-validation method to separate the data in training and test data and make the prediction. Cross-validation divides the initial dataset into a number of roughly equal parts (aka folds). In each round of the crossvalidation, each fold in turn is used as test data and the rest of the folds as training data. We use the Root Mean Squared Error (RMSE) of the log error to assess the result of Lasso. Log error is the log of the predicted value minus the log of the actual value.
In our case study we randomly select the folds used as test and trained data (using a seed). This means that each time someone repeats the same procedure with the same datasets, he/she will result in di erent train and test data and, hence, in di erent RMSE. We repeat the same Lasso analysis using the same datasets 100 times (which is also the default value for the gmlnet library) in order to see the variance of RMSEs during the multiple repetitions. Fig 1 presents two boxplots. The left boxplot illustrates the variance of the RMSE calculated in all 100 repeated Lasso experiments. We can see that the median of the RMSEs is close to 0.273 and that the distance between the median and the lower and upper quartiles is limited. The right boxplot presents the variation of the total number of the selected features based on one SE. We can see that the median number of features is 28 which is also the lower quartile. Cross-validation allows selecting the best value for the tuning parameter (lambda), or equivalently, the value of the constraints. To this end, we compute the lambda parameter. Lambda parameter controls the amount of regularization, so choosing a good value for it is crucial. In cases with very large number of features, lasso allows to e ciently nd the model that involves a small subset of the features. The value selected for lambda is the one that corresponds to the smallest error or the value with one standard error. The plot in Fig. 2 shows how the RMSE uctuates for di erent number of lambda (or features). Higher values of lambda produce less exible functions and, hence, higher errors while lower values of lambda produce more exible functions and, hence, lower errors. We select the optimal value for the lambda that corresponds to the minimum RMSE i.e. -4. Following this rule the nal number of selected features is 34.
We develop an open source tool as a proof of concept of the case study. The tool o ers an interface that facilitates the selection of compatible statistical datasets that can be used for machine learning analysis. The tool is based on R Shiny7 and obtains statistical datasets from the Scottish data portal. It allows selecting a dataset from the Scottish portal, and searches and presents compatible datasets based on the de ned compatibility criteria. The tool is available on GitHub 8.
Fig 3 presents a screen-shot of the Compatible LOSD Selection tool. On the left panel 2012 house prices has been selected as the rst dataset. On the right panel the 20 compatible datasets are presented. The selected compatible datasets can be extracted to contribute in the creation of a predictive model. Although governments and other organisations are continuously opening up their statistical data, the potential of open data has been unrealized to a large extent due to institutional and technical barriers. In machine learning analyses, linked data facilitate the discovery, retrieval, and combination of data on the Web. However, a challenge in such analyses is to specify the criteria to be considered in order to select the proper datasets to construct the predictive model.
In this paper we presented a case study that applied machine learning methods to compatible statistical datasets from the Scottish data portal in order to support advanced decision-making scenarios. The case study aimed to predict the house prices in Scotland. To facilitate the discovery of compatible datasets we dened ve compatibility criteria. Based on the criteria we discovered 21 datasets compatible with the response variable. From these datasets we extracted 450 features and applied the Lasso method in order to select the most important features. We resulted in 34 features coming from only 10 datasets (over 92% less features than the ones initially identi ed). This means that there is a strong relationship between the house prices in Scotland and these 10 datasets. We also developed the Compatible LOSD Selection tool that facilitates discovering compatible LOSD datasets to perform machine learning analysis.
This case study is indicative of the importance of using machine learning to analyse statistical datasets and support decision making. Starting from a problem that needed to be solved we resulted in identifying relationships between datasets, some of them previously unknown. For example, our case study revealed a strong relationship between the breastfeeding percentage and the mean house prices in Scotland. Other relationships were more obvious such as the one between Income and Poverty estimates and mean house prices. Eliminating in an easy way all irrelevant datasets can be really bene cial for decision makers as it saves them time from dealing with unessential data and help them understand which variables matter most and which can be ignored. More importantly, this case study proves that decision makers can yet easily exploit historical statistical data using machine learning in order to take evidence-based decisions.
The case study also proved that, when it comes to statistical data, e ectively discovering compatible datasets is crucial to be able to create successful predictive models. The compatibility criteria we de ned is only a rst attempt to de ne the compatibility between statistical datasets. However, this rst attempt proved that discovering compatible datasets forms the basis to extract meaningful results using machine learning.
Acknowledgments. This research is co- nanced by Greece and the European Union (European Social Fund- ESF) through the Operational Program \Human Resources Development, Education and Lifelong Learning 2014-2020" in the context of the project \Integrating open statistical data using semantic technologies" (MIS 5007306).