arXiv subjects

Antoine Amarilli

Publications and source records attributed to Antoine Amarilli.

67 records · Page 4Linked to original sources

arXiv2017

Top-k Querying of Unknown Values under Order Constraints (Extended Version)

Many practical scenarios make it necessary to evaluate top-k queries over data items with partially unknown values. This paper considers a setting where the values are taken from a numerical domain, and where some partial order constraints are given over known and unknown values: under these constraints, we assume that all possible worlds are equally likely. Our work is the first to propose a principled scheme to derive the value distributions and expected values of unknown items in this setting, with the goal of computing estimated top-k results by interpolating the unknown values from the known ones. We study the complexity of this general task, and show tight complexity bounds, proving that the problem is intractable, but can be tractably approximated. We then consider the case of tree-shaped partial orders, where we show a constructive PTIME solution. We also compare our problem setting to other top-k definitions on uncertain data.

cs.DB↗

arXiv2016

Predicting Completeness in Knowledge Bases

Knowledge bases such as Wikidata, DBpedia, or YAGO contain millions of entities and facts. In some knowledge bases, the correctness of these facts has been evaluated. However, much less is known about their completeness, i.e., the proportion of real facts that the knowledge bases cover. In this work, we investigate different signals to identify the areas where a knowledge base is complete. We show that we can combine these signals in a rule mining approach, which allows us to predict where facts may be missing. We also show that completeness predictions can help other applications such as fact prediction.

cs.DB↗

arXiv2016

Challenges for Efficient Query Evaluation on Structured Probabilistic Data

Query answering over probabilistic data is an important task but is generally intractable. However, a new approach for this problem has recently been proposed, based on structural decompositions of input databases, following, e.g., tree decompositions. This paper presents a vision for a database management system for probabilistic data built following this structural approach. We review our existing and ongoing work on this topic and highlight many theoretical and practical challenges that remain to be addressed.

cs.DB↗

arXiv2016

Query Answering with Transitive and Linear-Ordered Data

We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be transitive, restricting a relation to be the transitive closure of another relation, and restricting a relation to be a linear order. We give some natural generalizations of guardedness that allow inference to be decidable in each case, and isolate the complexity of the corresponding decision problems. Finally we show that slight changes in our conditions lead to undecidability.

cs.DB↗

arXiv2015

Provenance Circuits for Trees and Treelike Instances (Extended Version)

Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such as counting query results [3] or performing query evaluation on probabilistic trees [10]. These are two examples of the more general problem of computing augmented query output, that is referred to as provenance. This article presents a provenance framework for trees and treelike instances, by describing a linear-time construction of a circuit provenance representation for MSO queries. We show how this provenance can be connected to the usual definitions of semiring provenance on relational instances [20], even though we compute it in an unusual way, using tree automata; we do so via intrinsic definitions of provenance for general semirings, independent of the operational details of query evaluation. We show applications of this provenance to capture existing counting and probabilistic results on trees and treelike instances, and give novel consequences for probability evaluation.

cs.DB↗

arXiv2015

Structurally Tractable Uncertain Data

Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query possibility, certainty, or probability: these problems are hard on arbitrary uncertain input instances. We thus ask whether we could restrict the structure of uncertain data so as to guarantee the tractability of exact query evaluation. We present our tractability results for tree and tree-like uncertain data, and a vision for probabilistic rule reasoning. We also study uncertainty about order, proposing a suitable representation, and study uncertain data conditioned by additional observations.

cs.DB↗

arXiv2015

Finite Open-World Query Answering with Number Restrictions (Extended Version)

Open-world query answering is the problem of deciding, given a set of facts, conjunction of constraints, and query, whether the facts and constraints imply the query. This amounts to reasoning over all instances that include the facts and satisfy the constraints. We study finite open-world query answering (FQA), which assumes that the underlying world is finite and thus only considers the finite completions of the instance. The major known decidable cases of FQA derive from the following: the guarded fragment of first-order logic, which can express referential constraints (data in one place points to data in another) but cannot express number restrictions such as functional dependencies; and the guarded fragment with number restrictions but on a signature of arity only two. In this paper, we give the first decidability results for FQA that combine both referential constraints and number restrictions for arbitrary signatures: we show that, for unary inclusion dependencies and functional dependencies, the finiteness assumption of FQA can be lifted up to taking the finite implication closure of the dependencies. Our result relies on new techniques to construct finite universal models of such constraints, for any bound on the maximal query size.

cs.LO↗

arXiv2015

Harvesting Entities from the Web Using Unique Identifiers -- IBEX

In this paper we study the prevalence of unique entity identifiers on the Web. These are, e.g., ISBNs (for books), GTINs (for commercial products), DOIs (for documents), email addresses, and others. We show how these identifiers can be harvested systematically from Web pages, and how they can be associated with human-readable names for the entities at large scale. Starting with a simple extraction of identifiers and names from Web pages, we show how we can use the properties of unique identifiers to filter out noise and clean up the extraction result on the entire corpus. The end result is a database of millions of uniquely identified entities of different types, with an accuracy of 73--96% and a very high coverage compared to existing knowledge bases. We use this database to compute novel statistics on the presence of products, people, and other entities on the Web.

cs.DB↗

arXiv2015

Combining Existential Rules and Description Logics (Extended Version)

Query answering under existential rules -- implications with existential quantifiers in the head -- is known to be decidable when imposing restrictions on the rule bodies such as frontier-guardedness [BLM10, BLMS11]. Query answering is also decidable for description logics [Baa03], which further allow disjunction and functionality constraints (assert that certain relations are functions), however, they are focused on ER-type schemas, where relations have arity two. This work investigates how to get the best of both worlds: having decidable existential rules on arbitrary arity relations, while allowing rich description logics, including functionality constraints, on arity-two relations. We first show negative results on combining such decidable languages. Second, we introduce an expressive set of existential rules (frontier-one rules with a certain restriction) which can be combined with powerful constraints on arity-two relations (e.g. GC 2, ALCQIb) while retaining decidable query answering. Further, we provide conditions to add functionality constraints on the higher-arity relations.

cs.DB↗

arXiv2014

The Possibility Problem for Probabilistic XML (Extended Version)

We consider the possibility problem of determining if a document is a possible world of a probabilistic document, in the setting of probabilistic XML. This basic question is a special case of query answering or tree automata evaluation, but it has specific practical uses, such as checking whether an user-provided probabilistic document outcome is possible or sufficiently likely. In this paper, we study the complexity of the possibility problem for probabilistic XML models of varying expressiveness. We show that the decision problem is often tractable in the absence of long-distance dependencies, but that its computation variant is intractable on unordered documents. We also introduce an explicit matches variant to generalize practical situations where node labels are unambiguous; this ensures tractability of the possibility problem, even under long-distance dependencies, provided event conjunctions are disallowed. Our results entirely classify the tractability boundary over all considered problem variants.

cs.DB↗

arXiv2014

Uncertainty in Crowd Data Sourcing under Structural Constraints

Applications extracting data from crowdsourcing platforms must deal with the uncertainty of crowd answers in two different ways: first, by deriving estimates of the correct value from the answers; second, by choosing crowd questions whose answers are expected to minimize this uncertainty relative to the overall data collection goal. Such problems are already challenging when we assume that questions are unrelated and answers are independent, but they are even more complicated when we assume that the unknown values follow hard structural constraints (such as monotonicity). In this vision paper, we examine how to formally address this issue with an approach inspired by [Amsterdamer et al., 2013]. We describe a generalized setting where we model constraints as linear inequalities, and use them to guide the choice of crowd questions and the processing of answers. We present the main challenges arising in this setting, and propose directions to solve them.

cs.DB↗

arXiv2013

On the Complexity of Mining Itemsets from the Crowd Using Taxonomies

We study the problem of frequent itemset mining in domains where data is not recorded in a conventional database but only exists in human knowledge. We provide examples of such scenarios, and present a crowdsourcing model for them. The model uses the crowd as an oracle to find out whether an itemset is frequent or not, and relies on a known taxonomy of the item domain to guide the search for frequent itemsets. In the spirit of data mining with oracles, we analyze the complexity of this problem in terms of (i) crowd complexity, that measures the number of crowd questions required to identify the frequent itemsets; and (ii) computational complexity, that measures the computational effort required to choose the questions. We provide lower and upper complexity bounds in terms of the size and structure of the input taxonomy, as well as the size of a concise description of the output itemsets. We also provide constructive algorithms that achieve the upper bounds, and consider more efficient variants for practical situations.

cs.DB↗

arXiv2013

A Proof of the Pumping Lemma for Context-Free Languages Through Pushdown Automata

The pumping lemma for context-free languages is a result about pushdown automata which is strikingly similar to the well-known pumping lemma for regular languages. However, though the lemma for regular languages is simply proved by using the pigeonhole principle on deterministic automata, the lemma for pushdown automata is proven through an equivalence with context-free languages and through the more powerful Ogden's lemma. We present here a proof of the pumping lemma for context-free languages which relies on pushdown automata instead of context-free grammars.

cs.FL↗