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Yayın Mixture of Gaussian models and bayes error under differential privacy(2011) Xi, Bowei; Kantarcıoğlu, Murat; İnan, AliGaussian mixture models are an important tool in Bayesian decision theory. In this study, we focus on building such models over statistical database protected under differential privacy. Our approach involves querying necessary statistics from a database and building a Bayesian classifier over the noise added responses generated according to differential privacy. We formally analyze the sensitivity of our query set. Since there are multiple methods to query a statistic, either directly or indirectly, we analyze the sensitivities for different querying methods. Furthermore we establish theoretical bounds for the Bayes error for the univariate (one dimensional) case. We study the Bayes error for the multivariate (high dimensional) case in experiments with both simulated data and real life data. We discover that adding Laplace noise to a statistic under certain constraint is problematic. For example variance-covariance matrix is no longer positive definite after noise addition. We propose a heuristic method to fix the noise added variance-covariance matrix.Yayın Software defect prediction using Bayesian networks(Springer, 2014-02) Okutan, Ahmet; Yıldız, Olcay TanerThere are lots of different software metrics discovered and used for defect prediction in the literature. Instead of dealing with so many metrics, it would be practical and easy if we could determine the set of metrics that are most important and focus on them more to predict defectiveness. We use Bayesian networks to determine the probabilistic influential relationships among software metrics and defect proneness. In addition to the metrics used in Promise data repository, we define two more metrics, i.e. NOD for the number of developers and LOCQ for the source code quality. We extract these metrics by inspecting the source code repositories of the selected Promise data repository data sets. At the end of our modeling, we learn the marginal defect proneness probability of the whole software system, the set of most effective metrics, and the influential relationships among metrics and defectiveness. Our experiments on nine open source Promise data repository data sets show that response for class (RFC), lines of code (LOC), and lack of coding quality (LOCQ) are the most effective metrics whereas coupling between objects (CBO), weighted method per class (WMC), and lack of cohesion of methods (LCOM) are less effective metrics on defect proneness. Furthermore, number of children (NOC) and depth of inheritance tree (DIT) have very limited effect and are untrustworthy. On the other hand, based on the experiments on Poi, Tomcat, and Xalan data sets, we observe that there is a positive correlation between the number of developers (NOD) and the level of defectiveness. However, further investigation involving a greater number of projects is needed to confirm our findings.












