Infinite Probabilistic Databases

Grohe, Martin; Lindner, Peter

doi:10.46298/lmcs-18(1:34)2022

Cited by 8 publications

(20 citation statements)

References 38 publications

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“…Thus a view has a well-defined semantics on standard PDBs if and only if it is measurable. The following theorem, which is the main result of [12], states that this is the case for a wide class of views.…”

Section: Query Semanticsmentioning

confidence: 88%

“…A solution to this dilemma is a theoretical framework that gives us a generic construction of σ-algebras only depending on the schema τ and the universe U that is rich enough to make all sets that we typically want to consider measurable and at the same time ensures that all reasonable queries and views are measurable. Standard probabilistic databases, introduced in [12], provide such a framework.…”

Section: Standard Pdbsmentioning

confidence: 99%

“…Countably infinite TI PDBs were studied in [11]. An extension to uncountable PDBs, called Poisson PDBs, was proposed in [9]. Another basic model, block-independent disjoint (BID) PDBs, can also be extended to the infinite setting [11,9].…”

Section: Representationsmentioning

confidence: 99%

“…An extension to uncountable PDBs, called Poisson PDBs, was proposed in [9]. Another basic model, block-independent disjoint (BID) PDBs, can also be extended to the infinite setting [11,9]. Both TI and BID PDBs can only represent very simple probability distributions.…”

Section: Representationsmentioning

confidence: 99%

“…The flexibility of these systems reaches as far as providing declarative representations of continuous probabilistic databases and even continuous-space database-valued Markov processes. Yet, only recently [11,12], we proposed a general framework for rigorously dealing with probabilistic databases over continuous domains and provided a sound semantics for standard query languages such as the relational calculus. We will present this framework in Sections 4 and 5 of this paper.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Data with Continuous Distributions

Grohe¹,

Kaminski²,

Katoen³

et al. 2021

Preprint

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Statistical models of real world data typically involve continuous probability distributions such as normal, Laplace, or exponential distributions. Such distributions are supported by many probabilistic modelling formalisms, including probabilistic database systems. Yet, the traditional theoretical framework of probabilistic databases focusses entirely on finite probabilistic databases.Only recently, we set out to develop the mathematical theory of infinite probabilistic databases. The present paper is an exposition of two recent papers which are cornerstones of this theory. In (Grohe, Lindner; ICDT 2020) we propose a very general framework for probabilistic databases, possibly involving continuous probability distributions, and show that queries have a well-defined semantics in this framework. In (Grohe, Kaminski, Katoen, Lindner; PODS 2020) we extend the declarative probabilistic programming language Generative Datalog, proposed by (Bárány et al. 2017) for discrete probability distributions, to continuous probability distributions and show that such programs yield generative models of continuous probabilistic databases.

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Section: Query Semanticsmentioning

confidence: 88%

Section: Standard Pdbsmentioning

confidence: 99%

Section: Representationsmentioning

confidence: 99%

Section: Representationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Probabilistic Data with Continuous Distributions

Grohe¹,

Kaminski²,

Katoen³

et al. 2021

Preprint

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Independence in Infinite Probabilistic Databases

Grohe

Lindner

2022

J. ACM

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Probabilistic databases (PDBs) model uncertainty in data. The current standard is to view PDBs as finite probability spaces over relational database instances. Since many attributes in typical databases have infinite domains, such as integers, strings, or real numbers, it is often more natural to view PDBs as infinite probability spaces over database instances. In this paper, we lay the mathematical foundations of infinite probabilistic databases. Our focus then is on independence assumptions. Tuple-independent PDBs play a central role in theory and practice of PDBs. Here, we study infinite tuple-independent PDBs as well as related models such as infinite block-independent disjoint PDBs. While the standard model of PDBs focuses on a set-based semantics, we also study tuple-independent PDBs with a bag semantics and independence in PDBs over uncountable fact spaces. We also propose a new approach to PDBs with an open-world assumption, addressing issues raised by Ceylan et al. (Proc. KR 2016) and generalizing their work, which is still rooted in finite tuple-independent PDBs. Moreover, for countable PDBs we propose an approximate query answering algorithm.

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Generative Datalog with Continuous Distributions

Grohe

Kaminski

Katoen

et al. 2022

J. ACM

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Arguing for the need to combine declarative and probabilistic programming, Bárány et al. (TODS 2017) recently introduced a probabilistic extension of Datalog as a “purely declarative probabilistic programming language.” We revisit this language and propose a more principled approach towards defining its semantics based on stochastic kernels and Markov processes — standard notions from probability theory. This allows us to extend the semantics to continuous probability distributions, thereby settling an open problem posed by Bárány et al. We show that our semantics is fairly robust, allowing both parallel execution and arbitrary chase orders when evaluating a program. We cast our semantics in the framework of infinite probabilistic databases (Grohe and Lindner, LMCS 2022), and show that the semantics remains meaningful even when the input of a probabilistic Datalog program is an arbitrary probabilistic database.

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Infinite Probabilistic Databases

Cited by 8 publications

References 38 publications

Probabilistic Data with Continuous Distributions

Probabilistic Data with Continuous Distributions

Independence in Infinite Probabilistic Databases

Generative Datalog with Continuous Distributions

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