A Formal Framework for Probabilistic Unclean Databases

Authors Christopher De Sa, Ihab F. Ilyas, Benny Kimelfeld, Christopher Ré, Theodoros Rekatsinas

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Author Details

Christopher De Sa
  • Cornell University, Ithacan, NY, USA
Ihab F. Ilyas
  • University of Waterloo, Waterloo, ON, Canada
Benny Kimelfeld
  • Technion - Israel Institute of Technology, Haifa, Israel
Christopher Ré
  • Stanford University, Stanford, CA, USA
Theodoros Rekatsinas
  • University of Wisconsin - Madison, Madison, WI, USA

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Christopher De Sa, Ihab F. Ilyas, Benny Kimelfeld, Christopher Ré, and Theodoros Rekatsinas. A Formal Framework for Probabilistic Unclean Databases. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Most theoretical frameworks that focus on data errors and inconsistencies follow logic-based reasoning. Yet, practical data cleaning tools need to incorporate statistical reasoning to be effective in real-world data cleaning tasks. Motivated by empirical successes, we propose a formal framework for unclean databases, where two types of statistical knowledge are incorporated: The first represents a belief of how intended (clean) data is generated, and the second represents a belief of how noise is introduced in the actual observed database. To capture this noisy channel model, we introduce the concept of a Probabilistic Unclean Database (PUD), a triple that consists of a probabilistic database that we call the intention, a probabilistic data transformator that we call the realization and captures how noise is introduced, and an observed unclean database that we call the observation. We define three computational problems in the PUD framework: cleaning (infer the most probable intended database, given a PUD), probabilistic query answering (compute the probability of an answer tuple over the unclean observed database), and learning (estimate the most likely intention and realization models of a PUD, given examples as training data). We illustrate the PUD framework on concrete representations of the intention and realization, show that they generalize traditional concepts of repairs such as cardinality and value repairs, draw connections to consistent query answering, and prove tractability results. We further show that parameters can be learned in some practical instantiations, and in fact, prove that under certain conditions we can learn a PUD directly from a single dirty database without any need for clean examples.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data modeling
  • Theory of computation → Incomplete, inconsistent, and uncertain databases
  • Unclean databases
  • data cleaning
  • probabilistic databases
  • noisy channel


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