Processing lineages (also called provenances) over uncertain data consists in tracing the origin of uncertainty based on the process of data production and evolution. In this paper, we focus on the representation and processing of lineages over uncertain data, where we adopt Bayesian network (BN), one of the popular and important probabilistic graphical models (PGMs), as the framework of uncertainty representation and inferences. Starting from the lineage expressed as Boolean formulae for SPJ (Selection–Projection–Join) queries over uncertain data, we propose a method to transform the lineage expression into directed acyclic graphs (DAGs) equivalently. Specifically, we discuss the corresponding probabilistic semantics and properties to guarantee that the graphical model can support effective probabilistic inferences in lineage processing theoretically. Then, we propose the function-based method to compute the conditional probability table (CPT) for each node in the DAG. The BN for representing lineage expressions over uncertain data, called lineage BN and abbreviated as LBN, can be constructed while generally suitable for both safe and unsafe query plans. Therefore, we give the variable-elimination-based algorithm for LBN's exact inferences to obtain the probabilities of query results, called LBN-based query processing. Then, we focus on obtaining the probabilities of inputs or intermediate tuples conditioned on query results, called LBN-based inference query processing, and give the Gibbs-sampling-based algorithm for LBN's approximate inferences. Experimental results show the efficiency and effectiveness of our methods. 
Representing and processing lineages over uncertain data based on the Bayesian network