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Register a new userAssociative Arrays: Unified Mathematics for Spreadsheets, Databases, Matrices, and Graphs
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Added by
Jeremy Kepner
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. The common theme amongst these views is the need to store and operate on data as whole sets instead of as individual data elements. This work describes a common mathematical representation of these data sets (associative arrays) that applies across a wide range of applications and technologies. Associative arrays unify and simplify these different approaches for representing and manipulating data into common two-dimensional view of data. Specifically, associative arrays (1) reduce the effort required to pass data between steps in a data processing system, (2) allow steps to be interchanged with full confidence that the results will be unchanged, and (3) make it possible to recognize when steps can be simplified or eliminated. Most database system naturally support associative arrays via their tabular interfaces. The D4M implementation of associative arrays uses this feature to provide a common interface across SQL, NoSQL, and NewSQL databases.
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Probabilistic databases play a crucial role in the management and understanding of uncertain data. However, incorporating probabilities into the semantics of incomplete databases has posed many challenges, forcing systems to sacrifice modeling power, scalability, or restrict the class of relational algebra formula under which they are closed. We propose an alternative approach where the underlying relational database always represents a single world, and an external factor graph encodes a distribution over possible worlds; Markov chain Monte Carlo (MCMC) inference is then used to recover this uncertainty to a desired level of fidelity. Our approach allows the efficient evaluation of arbitrary queries over probabilistic databases with arbitrary dependencies expressed by graphical models with structure that changes during inference. MCMC sampling provides efficiency by hypothesizing {em modifications} to possible worlds rather than generating entire worlds from scratch. Queries are then run over the portions of the world that change, avoiding the onerous cost of running full queries over each sampled world. A significant innovation of this work is the connection between MCMC sampling and materialized view maintenance techniques: we find empirically that using view maintenance techniques is several orders of magnitude faster than naively querying each sampled world. We also demonstrate our systems ability to answer relational queries with aggregation, and demonstrate additional scalability through the use of parallelization.
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This paper addresses the problem of representing the set of repairs of a possibly inconsistent database by means of a disjunctive database. Specifically, the class of denial constraints is considered. We show that, given a database and a set of denial constraints, there exists a (unique) disjunctive database, called canonical, which represents the repairs of the database w.r.t. the constraints and is contained in any other disjunctive database with the same set of minimal models. We propose an algorithm for computing the canonical disjunctive database. Finally, we study the size of the canonical disjunctive database in the presence of functional dependencies for both repairs and cardinality-based repairs.
In the field of database deduplication, the goal is to find approximately matching records within a database. Blocking is a typical stage in this process that involves cheaply finding candidate pairs of records that are potential matches for further processing. We present here Hashed Dynamic Blocking, a new approach to blocking designed to address datasets larger than those studied in most prior work. Hashed Dynamic Blocking (HDB) extends Dynamic Blocking, which leverages the insight that rare matching values and rare intersections of values are predictive of a matching relationship. We also present a novel use of Locality Sensitive Hashing (LSH) to build blocking key values for huge databases with a convenient configuration to control the trade-off between precision and recall. HDB achieves massive scale by minimizing data movement, using compact block representation, and greedily pruning ineffective candidate blocks using a Count-min Sketch approximate counting data structure. We benchmark the algorithm by focusing on real-world datasets in excess of one million rows, demonstrating that the algorithm displays linear time complexity scaling in this range. Furthermore, we execute HDB on a 530 million row industrial dataset, detecting 68 billion candidate pairs in less than three hours at a cost of $307 on a major cloud service.
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