# Data Protection and Multi-Database Data-Driven Models
## 1 Introduction  
When personal data are used, we need to take into account privacy requirements. Current national and international regulations require companies to take privacy requirements seriously; see, e.g., GDPR, under which companies can be fined when disclosure of sensitive data takes place. Data cannot be shared freely with third parties when there is sensitive information. Nevertheless, it is not only the data that needs to satisfy privacy requirements, but also data-driven models built from these sensitive data. Privacy-by-design [1] states that privacy is not an add-on to systems processing data, but that privacy needs to be taken into account as a fundamental requirement of all the processes. Privacy technologies [2; 3; 4] have been developed to provide solutions that permit the sharing of data as well as building data-driven models that are compliant with our privacy requirements. There exist several privacy models, computational definitions of privacy, and alternative data protection mechanisms to implement the privacy models. Masking methods are tools that allow the data to be protected so that they can be shared with third parties without compromising sensitive data. Masking methods modify the original data, providing a sanitized version of a file or database, so that these sensitive data are not disclosed, and disclosure risk is minimized. As masking methods modify the original data, data utility is a major concern. Masking methods are typically parametric so that we can control the privacy level, or at least the perturbation level. The effects of masking methods on machine learning and statistics have been extensively studied [5; 6; 7]. A typical analysis consists of evaluating how different privacy levels affect the performance of data-driven models. This includes discovering which range of parameters results in an acceptable performance (e.g., accuracy or error) and which range of parameters causes the model to show unacceptable performance. Additionally, masking methods [8] have been compared in terms of performance for similar protection. Most of these comparisons are computational, testing the performance of the methods for particular data sets and particular machine learning algorithms. There is an increasing need to build more complex data-driven models. There is a need to use data from multiple databases, and once these data are integrated, data-driven models are built from the resulting databases. The effects of masking methods on data when these data are to be integrated is not known. In this paper, we study this problem. More specifically, we want to know  
* to what extent data integration is possible when data have been masked, and
* even if data integration cannot overcome the errors caused by masking methods and produces faulty databases, we want to know whether these databases are of high enough quality for data-driven models to be built. To achieve this goal, we conduct a series of controlled experiments. More precisely, given a database, we produce two different partial databases, which are protected separately and later integrated. Then, data-driven models are built from the integrated database. The results of the process are analyzed. We study the effects of different masking methods on different databases. We also consider the performance of alternative machine learning models. This paper is an extended version of a conference paper [9]. The paper is completely rewritten and we extend the experiments with additional databases, masking methods, parameterizations, and machine learning models. In fact, the software used for preparing this paper is also new, as previous experiments were performed in R and these ones were carried out in Python. A description of the software and a link to it are included below. The structure of the paper is as follows. In Section 2, we describe the main concepts we need in our paper. In Section 3 we present the methodology used. We formalize the process applied to a given database.