Sensitivity analysis and explanations for robust query evaluation in probabilistic databases

Abstract

Probabilistic database systems have successfully established themselves as a tool for managing uncertain data. However, much of the research in this area has focused on efficient query evaluation and has largely ignored two key issues that commonly arise in uncertain data management: First, how to provide explanations for query results, e.g., Why is this tuple in my result? or Why does this output tuple have such high probability?. Second, the problem of determining the sensitive input tuples for the given query, e.g., users are interested to know the input tuples that can substantially alter the output, when their probabilities are modified (since they may be unsure about the input probability values). Existing systems provide the lineage/provenance of each of the output tuples in addition to the output probabilities, which is a boolean formula indicating the dependence of the output tuple on the input tuples. However, lineage does not immediately provide a quantitative relationship and it is not informative when we have multiple output tuples. In this paper, we propose a unified framework that can handle both the issues mentioned above to facilitate robust query processing. We formally define the notions of influence and explanations and provide algorithms to determine the top-l influential set of variables and the top-l set of explanations for a variety of queries, including conjunctive queries, probabilistic threshold queries, top-k queries and aggregation queries. Further, our framework naturally enables highly efficient incremental evaluation when input probabilities are modified (e.g., if uncertainty is resolved). Our preliminary experimental results demonstrate the benefits of our framework for performing robust query processing over probabilistic databases.