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Added by
Max Willsey
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We present a new approach to e-matching based on relational join; in particular, we apply recent database query execution techniques to guarantee worst-case optimal run time. Compared to the conventional backtracking approach that always searches the e-graph top down, our new relational e-matching approach can better exploit pattern structure by searching the e-graph according to an optimized query plan. We also establish the first data complexity result for e-matching, bounding run time as a function of the e-graph size and output size. We prototyped and evaluated our technique in the state-of-the-art egg e-graph framework. Compared to a conventional baseline, relational e-matching is simpler to implement and orders of magnitude faster in practice.
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Variability inherently exists in databases in various contexts which creates database variants. For example, variants of a database could have different schemas/content (database evolution problem), variants of a database could root from different sources (data integration problem), variants of a database could be deployed differently for specific application domain (deploying a database for different configurations of a software system), etc. Unfortunately, while there are specific solutions to each of the problems arising in these contexts, there is no general solution that accounts for variability in databases and addresses managing variability within a database. In this paper, we formally define variational databases (VDBs) and statically-typed variational relational algebra (VRA) to query VDBs---both database and queries explicitly account for variation. We also design and implement variational database management system (VDBMS) to run variational queries over a VDB effectively and efficiently. To assess this, we generate two VDBs from real-world databases in the context of software development and database evolution with a set of experimental queries for each.
Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common subexpressions and fusible operators. The complex interaction among these properties impact on the execution cost poses a challenge to optimizing compilers. Existing compilers resort to intricate heuristics that complicate the codebase and add maintenance cost but fail to search through the large space of equivalent LA expressions to find the cheapest one. We introduce a general optimization technique for LA expressions, by converting the LA expressions into Relational Algebra (RA) expressions, optimizing the latter, then converting the result back to (optimized) LA expressions. One major advantage of this method is that it is complete, meaning that any equivalent LA expression can be found using the equivalence rules in RA. The challenge is the major size of the search space, and we address this by adopting and extending a technique used in compilers, called equality saturation. We integrate the optimizer into SystemML and validate it empirically across a spectrum of machine learning tasks; we show that we can derive all existing hand-coded optimizations in SystemML, and perform new optimizations that lead to speedups from 1.2X to 5X.
Causal inference is at the heart of empirical research in natural and social sciences and is critical for scientific discovery and informed decision making. The gold standard in causal inference is performing randomized controlled trials; unfortunately these are not always feasible due to ethical, legal, or cost constraints. As an alternative, methodologies for causal inference from observational data have been developed in statistical studies and social sciences. However, existing methods critically rely on restrictive assumptions such as the study population consisting of homogeneous elements that can be represented in a single flat table, where each row is referred to as a unit. In contrast, in many real-world settings, the study domain naturally consists of heterogeneous elements with complex relational structure, where the data is naturally represented in multiple related tables. In this paper, we present a formal framework for causal inference from such relational data. We propose a declarative language called CaRL for capturing causal background knowledge and assumptions and specifying causal queries using simple Datalog-like rules.CaRL provides a foundation for inferring causality and reasoning about the effect of complex interventions in relational domains. We present an extensive experimental evaluation on real relational data to illustrate the applicability of CaRL in social sciences and healthcare.
Learning novel concepts and relations from relational databases is an important problem with many applications in database systems and machine learning. Relational learning algorithms learn the definition of a new relation in terms of existing relations in the database. Nevertheless, the same data set may be represented under different schemas for various reasons, such as efficiency, data quality, and usability. Unfortunately, the output of current relational learning algorithms tends to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency. This variation complicates their off-the-shelf application. In this paper, we introduce and formalize the property of schema independence of relational learning algorithms, and study both the theoretical and empirical dependence of existing algorithms on the common class of (de) composition schema transformations. We study both sample-based learning algorithms, which learn from sets of labeled examples, and query-based algorithms, which learn by asking queries to an oracle. We prove that current relational learning algorithms are generally not schema independent. For query-based learning algorithms we show that the (de) composition transformations influence their query complexity. We propose Castor, a sample-based relational learning algorithm that achieves schema independence by leveraging data dependencies. We support the theoretical results with an empirical study that demonstrates the schema dependence/independence of several algorithms on existing benchmark and real-world datasets under (de) compositions.
Financial transactions, internet search, and data analysis are all placing increasing demands on databases. SQL, NoSQL, and NewSQL databases have been developed to meet these demands and each offers unique benefits. SQL, NoSQL, and NewSQL databases also rely on different underlying mathematical models. Polystores seek to provide a mechanism to allow applications to transparently achieve the benefits of diverse databases while insulating applications from the details of these databases. Integrating the underlying mathematics of these diverse databases can be an important enabler for polystores as it enables effective reasoning across different databases. Associative arrays provide a common approach for the mathematics of polystores by encompassing the mathematics found in different databases: sets (SQL), graphs (NoSQL), and matrices (NewSQL). Prior work presented the SQL relational model in terms of associative arrays and identified key mathematical properties that are preserved within SQL. This work provides the rigorous mathematical definitions, lemmas, and theorems underlying these properties. Specifically, SQL Relational Algebra deals primarily with relations - multisets of tuples - and operations on and between these relations. These relations can be modeled as associative arrays by treating tuples as non-zero rows in an array. Operations in relational algebra are built as compositions of standard operations on associative arrays which mirror their matrix counterparts. These constructions provide insight into how relational algebra can be handled via array operations. As an example application, the composition of two projection operations is shown to also be a projection, and the projection of a union is shown to be equal to the union of the projections.
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