19,471 research outputs found
Infinite Probabilistic Databases
Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009).
We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics.
It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries
Provenance for Aggregate Queries
We study in this paper provenance information for queries with aggregation.
Provenance information was studied in the context of various query languages
that do not allow for aggregation, and recent work has suggested to capture
provenance by annotating the different database tuples with elements of a
commutative semiring and propagating the annotations through query evaluation.
We show that aggregate queries pose novel challenges rendering this approach
inapplicable. Consequently, we propose a new approach, where we annotate with
provenance information not just tuples but also the individual values within
tuples, using provenance to describe the values computation. We realize this
approach in a concrete construction, first for "simple" queries where the
aggregation operator is the last one applied, and then for arbitrary (positive)
relational algebra queries with aggregation; the latter queries are shown to be
more challenging in this context. Finally, we use aggregation to encode queries
with difference, and study the semantics obtained for such queries on
provenance annotated databases
ï»żAn Answer Explanation Model for Probabilistic Database Queries
Following the availability of huge amounts of uncertain data, coming from diverse ranges of applications such as sensors, machine learning or mining approaches, information extraction and integration, etc. in recent years, we have seen a revival of interests in probabilistic databases. Queries over these databases result in probabilistic answers. As the process of arriving at these answers is based on the underlying stored uncertain data, we argue that from the standpoint of an end user, it is helpful for such a system to give an explanation on how it arrives at an answer and on which uncertainty assumptions the derived answer is based. In this way, the user with his/her own knowledge can decide how much confidence to place in this probabilistic answer. \ud
The aim of this paper is to design such an answer explanation model for probabilistic database queries. We report our design principles and show the methods to compute the answer explanations. One of the main contributions of our model is that it fills the gap between giving only the answer probability, and giving the full derivation. Furthermore, we show how to balance verifiability and influence of explanation components through the concept of verifiable views. The behavior of the model and its computational efficiency are demonstrated through an extensive performance study
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