Efficient Discovery of Conditional Dependencies with Desbordante

Data profiling aims to extract complex patterns from data for further analysis and use that data in domains such as data cleaning, data deduplication, anomaly detection, and many more. Functional dependencies (FDs) are one of the most well-known patterns. However, they are poorly suited for these tasks, as real data is usually dirty, and the rigid definition of FDs does not allow algorithms to locate them. For this reason, there are several formulations aimed at relaxing FDs to support dirty data, with approximate functional dependency (AFD) being the most popular one. Another formulation is the Probabilistic Functional Dependency (pFD), which we aim to support inside Desbordante - a science-intensive, high-performance and open-source data profiling tool implemented in C++. However, pFDs are relatively poorly studied, compared to AFDs. In this paper we study pFDs, both analytically and empirically. We start by assessing how different pFDs and AFDs are by studying cases in which pFDs have an edge over AFDs. Then, we implement the algorithm for pFD discovery, as well as study its run time and memory consumption. We also compare it with an AFD discovery algorithm. Lastly, we study the output of both algorithms to learn whether or not it is possible to use AFD discovery algorithm to get pFDs and vice versa.

Inclusion dependency is a relation between attributes of tables that indicates possible Primary Key-Foreign Key references. Automatic discovery of inclusion dependencies is a relevant problem for both academic and industrial communities. The core concern for this problem is the efficiency of discovery process, since it is a computationally expensive task. However, existing studies only address the algorithmic side, while leaving out the implementation aspect. At the same time, engineering details are at least as important as the algorithmic ones for achieving good performance. In this paper, we describe techniques for efficient implementation of two algorithms for discovery of inclusion dependencies - Spider and Faida. The first one is a classic algorithm whose ideas lie in the foundation of many other inclusion dependency discovery algorithms. We propose an efficient parallelization technique, which greatly speeds up the algorithm while simultaneously reducing its memory consumption. The second one is the state-of-the-art approximate algorithm, which we approach by applying four types of optimizations: data buffering, SIMD-enabled execution, careful hash-table selection and parallelization. In order to experimentally evaluate our techniques, we have implemented these algorithms in Desbordante - an open-source science-intensive data profiler written in C++. For Spider, we have evaluated several different options, and in case of Faida we have demonstrated that all our optimization techniques yield results. We also compared our implementations with Metanome - a Java-based data profiler. Overall, we report up to 5x improvement in terms of run time reduction for Spider and up to 8x for Faida.

Matching dependency is a generalization of the functional dependency concept, which allows users to apply custom similarity functions for matching individual attributes. Matching dependencies have a wide range of applications for solving various data quality problems, such as entity resolution, data deduplication, data integration, schema matching, and many more. However, their discovery is a very computationally intensive problem, which limits their practical application. In this paper, we describe a number of optimization techniques for HyMD - currently the state-of-the-art algorithm for the discovery of matching dependencies. These optimizations belong to both technical and scientific domains. The most important of them are: 1) a new sampling technique, 2) a faster generalization lookup technique, and 3) an improved representation of a dependency. The first one aims to raise the efficiency of inference from record pairs, while the last two are designed to speed up lattice-related operations. To evaluate our optimizations, we implemented our version of HyMD in Desbordante, an open-source high-performance data profiler. Experiments demonstrated that they allow for a speedup of more than 40x over the state-of-the-art implementation on average, reaching a speedup greater than 170x in some cases. Finally, the improved version of HyMD is ready to use by anyone. It comes with bidirectional Python integration, which allows calling the C++ algorithm implementation from Python programs while allowing users to supply their custom matching functions.