Declarative Probabilistic Programming with Datalog

Bárány, Vince; Cate, Balder ten; Kimelfeld, Benny; Olteanu, Dan; Vagena, Zografoula

doi:10.1145/3132700

Cited by 34 publications

(71 citation statements)

References 54 publications

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“…Let F be a collection of disjoint measurable fact sets. It has to be shown that the events (E F ) F ∈F are independent (i. e., (7) holds). To see this, we show the independence of (E F ) F ∈F ′ where E F = Ω − E f .…”

Section: Tuple-independence In the Infinitementioning

confidence: 99%

Probabilistic Databases with an Infinite Open-World Assumption

Grohe

Lindner

2019

Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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Probabilistic databases (PDBs) introduce uncertainty into relational databases by specifying probabilities for several possible instances. Traditionally, they are finite probability spaces over database instances. Such finite PDBs inherently make a closed-world assumption: non-occurring facts are assumed to be impossible, rather than just unlikely. As convincingly argued by Ceylan et al. (KR '16), this results in implausibilities and clashes with intuition. An open-world assumption, where facts not explicitly listed may have a small positive probability can yield more reasonable results. The corresponding open-world model of Ceylan et al., however, assumes that all entities in the PDB come from a fixed finite universe.In this work, we take one further step and propose a model of "truly" open-world PDBs with an infinite universe. This is natural when we consider entities from typical domains such as integers, real numbers, or strings. While the probability space might become infinitely large, all instances of a PDB remain finite. We provide a sound mathematical framework for infinite PDBs generalizing the existing theory of finite PDBs. Our main results are concerned with countable, tuple-independent PDBs; we present a generic construction showing that such PDBs exist in the infinite and provide a characterization of their existence. This construction can be used to give an open-world semantics to finite PDBs. The construction can also be extended to so-called block-independent-disjoint probabilistic databases.Algorithmic questions are not the focus of this paper, but we show how query evaluation algorithms can be lifted from finite PDBs to perform approximate evaluation (with an arbitrarily small additive approximation error) in countably infinite tuple-independent PDBs.

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Section: Tuple-independence In the Infinitementioning

confidence: 99%

Probabilistic Databases with an Infinite Open-World Assumption

Grohe

Lindner

2019

Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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“…As discussed in detail later in Section 6, we believe that modern needs require the enhancement of the database technology with machine learning capabilities. In particular, an important challenge is to combine the two key capabilities (machine learning and data) via query languages for building statistical models, as already began by initial efforts [23,35]. Reasoning.…”

Section: Rdbms Technology In the Presence Of Incomplete Datamentioning

confidence: 99%

“…For example, by applying the notion of the Vapnik-Chervonenkis dimension, an important theoretical concept in generalization theory, to database queries, Riondato et al [121] provide accurate bounds for their selectivity estimates that hold with high probability; moreover, they show the error probability to hold simultaneously for the selectivity estimates of all queries in the query class. In general, this direction can leverage the past decade of research on probabilistic databases [47,90,23,91], which can be combined with theoretical frameworks of machine learning, such as PAC (Probably Approximately Correct) learning [139].…”

Section: Data Management and Machine Learningmentioning

confidence: 99%

Research Directions for Principles of Data Management (Abridged)

Abiteboul¹,

Arenas²,

Barceló³

et al. 2017

SIGMOD Rec.

Self Cite

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Research directions for Principles of Data ManagementPDM played a foundational role in the relational database model, with the robust connection between algebraic and calculus-based query languages, the connection between integrity constraints and database design, key insights for the field of query optimization, and the fundamentals of consistent concurrent transactions. This early work included rich cross-fertilization between PDM and other disciplines in mathematics and computer science, including logic, complexity theory, and knowledge representation. Since the 1990s we have seen an overwhelming increase in both the production of data and the ability to store and access such data. This has led to a phenomenal metamorphosis in the ways that we manage and use data. During this time, we have gone (1) from stand-alone disk-based databases to data that is spread across and linked by the Web, (2) from rigidly structured towards loosely structured data, and (3) from relational data to many different data models (hierarchical, graph-structured, data points, NoSQL, text data, image data, etc.). Research on PDM has developed during that time, too, following, accompanying and influencing this process. It has intensified research on extensions of the relational model (data exchange, incomplete data, probabilistic data, . . . ), on other data models (hierachical, semi-structured, graph, text, . . . ), and on a variety of further data management areas, including knowledge representation and the semantic web, data privacy and security, and data-aware (business) processes. Along the way, the PDM community expanded its cross-fertilization with related areas, to include automata theory, web services, parallel computation, document processing, data structures, scientific workflow, business process management, data-centered dynamic systems, data mining, machine learning, information extraction, etc.Looking forward, three broad areas of data management stand out where principled, mathematical thinking can bring new approaches and much-needed clarity. The first relates to the full lifecycle of so-called "Big Data Analytics", that is, the application of statistical and machine learning techniques to make sense out of, and derive value from, massive volumes of data. The second stems from new forms of data creation and processing, especially as it arises in applications such as web-based commerce, social media applications, and dataaware workflow and business process management. The third, which is just beginning to emerge, is the development of new principles and approaches in support of ethical data management. We briefly illustrate some of the primary ways that these three areas can be supported by the seven PDM research themes that are explored in this report.The overall lifecycle of Big Data Analytics raises a wealth of challenge areas that PDM can help with. As documented in numerous sources, so-called "data wrangling" can form 50% to 80% of the labor costs in an analytics investigation. The challenges of data wrangling can be ...

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“…InsideOut is a component of LogicBlox's effort to extend LogiQL to be a probabilistic programming language [10], as part of DARPA's PPAML and MUSE programs. The component the algorithm handles is inference in discrete graphical models.…”

Section: Practical Implicationsmentioning

confidence: 99%

Juggling Functions Inside a Database

Khamis¹,

Ngo²,

Rudra

2017

SIGMOD Rec.

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We define and study the Functional Aggregate Query (FAQ) problem, which captures common computational tasks across a very wide range of domains including relational databases, logic, matrix and tensor computation, probabilistic graphical models, constraint satisfaction, and signal processing. Simply put, an FAQ is a declarative way of defining a new function from a database of input functions.We present InsideOut, a dynamic programming algorithm, to evaluate an FAQ. The algorithm rewrites the input query into a set of easier-to-compute FAQ sub-queries. Each subquery is then evaluated using a worst-case optimal relational join algorithm. The topic of designing algorithms to optimally evaluate the classic multiway join problem has seen exciting developments in the past few years. Our framework tightly connects these new ideas in database theory with a vast number of application areas in a coherent manner, showing potentially that -with the right abstraction, blurring the distinction between data and computation -a good database engine can be a general purpose constraint solver, relational data store, graphical model inference engine, and matrix/tensor computation processor all at once.The InsideOut algorithm is very simple, as shall be described in this paper. Yet, in spite of solving an extremely general problem, its runtime either is as good as or improves upon the best known algorithm for the applications that FAQ specializes to. These corollaries include computational tasks in graphical model inference, matrix/tensor operations, relational joins, and logic. Better yet, InsideOut can be used within any database engine, because it is basically a principled way of rewriting queries. Indeed, it is already part of the LogicBlox database engine, helping efficiently answer traditional database queries, graphical model inference queries, and train a large class of machine learning models inside the database itself.

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Declarative Probabilistic Programming with Datalog

Cited by 34 publications

References 54 publications

Probabilistic Databases with an Infinite Open-World Assumption

Probabilistic Databases with an Infinite Open-World Assumption

Research Directions for Principles of Data Management (Abridged)

Juggling Functions Inside a Database

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