Online Appendix to Domain-Independent Data Cleaning via Analysis of Entity-Relationship Graph

Notation. We will compute probabilities of certain events. Notation P(A) refers to the probability of event A to occur. We use E to denote event “E exists” for an edge E. Similarly, we use E 6∃ for event “E does not exist”. Therefore, P(E) refers to the probability that E exists. We will consider situations where the algorithm computes the probability of following (or, ‘going along’) a specific edge E, usually in the context of a specific path. This probability is denoted as P(E ). We will use dep(e1, e2) notation as follows: dep(e1, e2) = true if and only if events e1 and e2 are dependent. Notation P denote the path being currently considered. Table I summarizes the notation. The challenge. Figure 1 illustrates an interesting property of graphs with probabilistic edges: each such graph maps on to a family of regular graphs. Figure 1(a) shows a probabilistic graph where three edges are labeled with probability of 0.5. This probabilistic graph maps on to 2 regular graphs. For instance, if we assume that none of the three edges is present (the probability of which is 0.5) then the graph in 1(a) will be instantiated to the regular graph in Figure 1(b). Figures 1(c) and 1(d) show other two possible instantiations of it, each having the same probability of occurring of 0.5. The challenge in designing algorithms that compute any measure on such probabilistic graphs, including the connection strength measure, comes from the following observation. If a probabilistic graph has n independent edges, that are labeled with non-1 probabilities, then this graph maps into the exponential number (i.e., 2) of regular graphs, where the probability of each instantiation is determined by the probability of the corresponding combination of edges to exist. Algorithms that work with probabilistic graphs should be able to account for the fact that some of the edges exist only with certain probabilities. If such an algorithm computes a certain measure on a probabilistic graph it should avoid computing it näıvly by com-