@techreport{TD:101698, att_abstract={{Quantitative data cleaning relies on the use of statistical methods to identify and repair data quality problems while logical data cleaning tackles the same problems using various forms of logical reasoning over declarative dependencies. Each of these approaches has its strengths: the logical approach is able to capture subtle data quality problems using sophisticated dependencies, while the quantitative approach excels at ensuring that the repaired data has desired statistical properties. We propose a novel framework within which these two approaches can be used synergistically to combine their respective strengths. We instantiate our framework using (i) metric functional dependencies (metric FDs), a type of dependency that generalizes the commonly used FDs to identify inconsistencies in domains where only large differences in metric data are considered to be a data quality problem, and (ii) repairs that modify the inconsistent data so as to minimize statistical distortion, measured using the Earth Mover's Distance (EMD). We show that the problem of computing a statistical distortion minimal repair is NP-hard. Given this complexity, we present an efficient algorithm for finding a minimal repair that has a small statistical distortion using EMD computation over semantically related attributes. To identify semantically related attributes, we present a sound and complete axiomatization and an efficient algorithm for testing implication of metric FDs. While the complexity of inference for some other FD extensions is co-NP complete, we show that the inference problem for metric FDs remains linear, as in traditional FDs. We prove that every instance that can be generated by our repair algorithm is set minimal (with no redundant changes). Our experimental evaluation demonstrates that our techniques obtain a considerably lower statistical distortion than existing repair techniques, while achieving similar levels of efficiency.}}, att_authors={ds8961}, att_categories={C_IIS.6}, att_copyright={{VLDB Foundation}}, att_copyright_notice={{The definitive version was published in Very Large Databases, 2015. {{, 2015-11-30}} }}, att_donotupload={}, att_private={false}, att_projects={}, att_tags={}, att_techdoc={true}, att_techdoc_key={TD:101698}, att_url={http://web1.research.att.com:81/techdocs_downloads/TD:101698_DS1_2015-12-01T14:33:28.216Z.pdf}, author={Divesh Srivastava and Nataliya Prokoshyna and Jaroslaw Szlichta and Fei Chiang and Renee J. Miller}, institution={{Proceedings of the VLDB Endowment}}, month={November}, title={{Combining Quantitative and Logical Data Cleaning}}, year=2015, }