Contribution Maximization in Probabilistic Datalog

Abstract

The use of probabilistic datalog programs has been recently advocated for applications that involve recursive computation and uncertainty. While using such programs allows for a flexible knowledge derivation, it makes the analysis of query results a challenging task. Particularly, given a set O of output tuples and a number k, one would like to understand which k-size subset of the input tuples have contributed the most to the derivation of O. This is useful for multiple tasks, such as identifying the critical sources of errors and understanding surprising results. Previous works have mainly focused on the quantification of tuples contribution to a query result in non-recursive SQL queries, very often disregarding probabilistic inference. To quantify the contribution in probabilistic datalog programs, one must account for the recursive relations between input and output data, and the uncertainty. To this end, we formalize the Contribution Maximization (CM) problem. We then reduce CM to the well-studied Influence Maximization (IM) problem, showing that we can harness techniques developed for IM to our setting. However, we show that such naïve adoption results in poor performance. To overcome this, we propose an optimized algorithm which injects a refined variant of the classic Magic Sets technique, integrated with a sampling method, into IM algorithms, achieving a significant saving of space and execution time. Our experiments demonstrate the effectiveness of our algorithm, even where the naïve approach is infeasible.