We study the complexity of evaluating queries on probabilistic databases under bag semantics. We focus on self-join free conjunctive queries, and probabilistic databases where occurrences of different facts are independent, which is the natural generalization of tuple-independent probabilistic databases to the bag semantics setting. For set semantics, the data complexity of this problem is well understood, even for the more general class of unions of conjunctive queries: it is either in polynomial time, or #P-hard, depending on the query (Dalvi & Suciu, JACM 2012).
A reasonably general model of bag probabilistic databases may have unbounded multiplicities. In this case, the probabilistic database is no longer finite, and a careful treatment of representation mechanisms is required. Moreover, the answer to a Boolean query is a probability distribution over (possibly all) non-negative integers, rather than a probability distribution over { true, false }. Therefore, we discuss two flavors of probabilistic query evaluation: computing expectations of answer tuple multiplicities, and computing the probability that a tuple is contained in the answer at most k times for some parameter k. Subject to mild technical assumptions on the representation systems, it turns out that expectations are easy to compute, even for unions of conjunctive queries. For query answer probabilities, we obtain a dichotomy between solvability in polynomial time and #P-hardness for self-join free conjunctive queries.
In database-as-a-service platforms, automated verification of query equivalence helps eliminate redundant computation in the form of overlapping sub-queries. Researchers have proposed two pragmatic techniques to tackle this problem. The first approach consists of reducing the queries to algebraic expressions and proving their equivalence using an algebraic theory. The limitations of this technique are threefold. It cannot prove the equivalence of queries with significant differences in the attributes of their relational operators. It does not support certain widely-used SQL features. Its verif…
We consider the problem of finding equivalent minimal-size reformulations of SQL queries in presence of embedded dependencies [1]. Our focus is on select-project-join (SPJ) queries with equality comparisons, also known as safe conjunctive (CQ) queries, possibly with grouping and aggregation. For SPJ queries, the semantics of the SQL standard treat query answers as multisets (a.k.a. bags), whereas the stored relations may be treated either as sets, which is called bag-set semantics for query evaluation, or as bags, which is called bag semantics. (Under set semantics, both query answers and stor…
The query containment problem is a fundamental algorithmic problem in data management. While this problem is well understood under set semantics, it is by far less understood under bag semantics. In particular, it is a long-standing open question whether or not the conjunctive query containment problem under bag semantics is decidable. We unveil tight connections between information theory and the conjunctive query containment under bag semantics. These connections are established using information inequalities, which are considered to be the laws of information theory. Our first main result a…
In their classical 1993 paper [CV93] Chaudhuri and Vardi notice that some fundamental database theory results and techniques fail to survive when we try to see query answers as bags (multisets) of tuples rather than as sets of tuples. But disappointingly, almost 30 years after [CV93], the bag-semantics based database theory is still in its infancy. We do not even know whether conjunctive query containment is decidable. And this is not due to lack of interest, but because, in the multiset world, everything suddenly gets discouragingly complicated. In this paper, we try to re-examine, in the bag…
In this paper we show that the chase technique is powerful enough to capture the bag-set semantics of conjunctive queries over IDBs and IDs and TGDs. In addition, we argue that in such cases it provides efficient (LogSpace) query evaluation algorithms and that, moreover, it can serve as a basis for evaluating some restricted classes of aggregate queries under incomplete information.
The conservativity theorem for nested relational calculus implies that query expressions can freely use nesting and unnesting, yet as long as the query result type is a flat relation, these capabilities do not lead to an increase in expressiveness over flat relational queries. Moreover, Wong showed how such queries can be translated to SQL via a constructive rewriting algorithm. While this result holds for queries over either set or multiset semantics, to the best of our knowledge, the questions of conservativity and normalization have not been studied for queries that mix set and bag collecti…
In this work, we study the problem of computing a tuple's expected multiplicity over probabilistic databases with bag semantics (where each tuple is associated with a multiplicity) exactly and approximately. We consider bag-TIDBs where we have a bound $c$ on the maximum multiplicity of each tuple and tuples are independent probabilistic events (we refer to such databases as c-TIDBs. We are specifically interested in the fine-grained complexity of computing expected multiplicities and how it compares to the complexity of deterministic query evaluation algorithms -- if these complexities are com…
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.
We show that for every conjunctive query, the complexity of evaluating it on a probabilistic database is either \PTIME or #¶-complete, and we give an algorithm for deciding whether a given conjunctive query is \PTIME or #¶-complete. The dichotomy property is a fundamental result on query evaluation on probabilistic databases and it gives a complete classification of the complexity of conjunctive queries.
We present EntropyDB, an interactive data exploration system that uses a probabilistic approach to generate a small, query-able summary of a dataset. Departing from traditional summarization techniques, we use the Principle of Maximum Entropy to generate a probabilistic representation of the data that can be used to give approximate query answers. We develop the theoretical framework and formulation of our probabilistic representation and show how to use it to answer queries. We then present solving techniques, give two critical optimizations to improve preprocessing time and query execution t…
The probabilistic threshold query is one of the most common queries in uncertain databases, where a result satisfying the query must be also with probability meeting the threshold requirement. In this paper, we investigate probabilistic threshold keyword queries (PrTKQ) over XML data, which is not studied before. We first introduce the notion of quasi-SLCA and use it to represent results for a PrTKQ with the consideration of possible world semantics. Then we design a probabilistic inverted (PI) index that can be used to quickly return the qualified answers and filter out the unqualified ones b…
A large spectrum of applications such as location based services and environmental monitoring demand efficient query processing on uncertain databases. In this paper, we propose the probabilistic Voronoi diagram (PVD) for processing moving nearest neighbor queries on uncertain data, namely the probabilistic moving nearest neighbor (PMNN) queries. A PMNN query finds the most probable nearest neighbor of a moving query point continuously. To process PMNN queries efficiently, we provide two techniques: a pre-computation approach and an incremental approach. In the pre-computation approach, we dev…
We address the issue of incorporating a particular yet expressive form of integrity constraints (namely, denial constraints) into probabilistic databases. To this aim, we move away from the common way of giving semantics to probabilistic databases, which relies on considering a unique interpretation of the data, and address two fundamental problems: consistency checking and query evaluation. The former consists in verifying whether there is an interpretation which conforms to both the marginal probabilities of the tuples and the integrity constraints. The latter is the problem of answering que…
RelationalAI Inc.（RelationalAI公司）；Carleton University（卡尔顿大学）；University of Oxford（牛津大学）；TU Wien（维也纳技术大学）
Duplicates in data management are common and problematic. In this work, we present a translation of Datalog under bag semantics into a well-behaved extension of Datalog, the so-called {\em warded Datalog}$^\pm$, under set semantics. From a theoretical point of view, this allows us to reason on bag semantics by making use of the well-established theoretical foundations of set semantics. From a practical point of view, this allows us to handle the bag semantics of Datalog by powerful, existing query engines for the required extension of Datalog. This use of Datalog$^\pm$ is extended to give a se…
Most of the work on query evaluation in probabilistic databases has focused on the simple tuple-independent data model, where tuples are independent random events. Several efficient query evaluation techniques exists in this setting, such as safe plans, algorithms based on OBDDs, tree-decomposition and a variety of approximation algorithms. However, complex data analytics tasks often require complex correlations, and query evaluation then is significantly more expensive, or more restrictive. In this paper, we propose MVDB as a framework both for representing complex correlations and for effici…
As probabilistic data management is becoming one of the main research focuses and keyword search is turning into a more popular query means, it is natural to think how to support keyword queries on probabilistic XML data. With regards to keyword query on deterministic XML documents, ELCA (Exclusive Lowest Common Ancestor) semantics allows more relevant fragments rooted at the ELCAs to appear as results and is more popular compared with other keyword query result semantics (such as SLCAs). In this paper, we investigate how to evaluate ELCA results for keyword queries on probabilistic XML docume…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the complexity, these known tractable cases usually do not apply to combined complexity, i.e., when the query is not fixed. This leaves open the question of which query and instance languages ensure the tractability of probabilistic query evaluation in combined complexity. This paper proposes the first general study of the combined complexity of conjunctive que…
Knowledge graphs (KG) that model the relationships between entities as labeled edges (or facts) in a graph are mostly constructed using a suite of automated extractors, thereby inherently leading to uncertainty in the extracted facts. Modeling the uncertainty as probabilistic confidence scores results in a probabilistic knowledge graph. Graph queries over such probabilistic KGs require answer computation along with the computation of those result probabilities, aka, probabilistic inference. We propose a system, HAPPI (How Provenance of Probabilistic Inference), to handle such query processing.…
We present a probabilistic approach to generate a small, query-able summary of a dataset for interactive data exploration. Departing from traditional summarization techniques, we use the Principle of Maximum Entropy to generate a probabilistic representation of the data that can be used to give approximate query answers. We develop the theoretical framework and formulation of our probabilistic representation and show how to use it to answer queries. We then present solving techniques and give three critical optimizations to improve preprocessing time and query accuracy. Lastly, we experimental…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We propose unifying techniques from probabilistic databases and relational embedding models with the goal of performing complex queries on incomplete and uncertain data. We formalize a probabilistic database model with respect to which all queries are done. This allows us to leverage the rich literature of theory and algorithms from probabilistic databases for solving problems. While this formalization can be used with any relational embedding model, the lack of a well-defined joint probability distribution causes simple query problems to become provably hard. With this in mind, we introduce \…
A boolean expression is in read-once form if each of its variables appears exactly once. When the variables denote independent events in a probability space, the probability of the event denoted by the whole expression in read-once form can be computed in polynomial time (whereas the general problem for arbitrary expressions is #P-complete). Known approaches to checking read-once property seem to require putting these expressions in disjunctive normal form. In this paper, we tell a better story for a large subclass of boolean event expressions: those that are generated by conjunctive queries w…
In query optimisation accurate cardinality estimation is essential for finding optimal query plans. It is especially challenging for RDF due to the lack of explicit schema and the excessive occurrence of joins in RDF queries. Existing approaches typically collect statistics based on the counts of triples and estimate the cardinality of a query as the product of its join components, where errors can accumulate even when the estimation of each component is accurate. As opposed to existing methods, we propose PRESTO, a cardinality estimation method that is based on the counts of subgraphs instead…
We address the problem of finding a "best" deterministic query answer to a query over a probabilistic database. For this purpose, we propose the notion of a consensus world (or a consensus answer) which is a deterministic world (answer) that minimizes the expected distance to the possible worlds (answers). This problem can be seen as a generalization of the well-studied inconsistent information aggregation problems (e.g. rank aggregation) to probabilistic databases. We consider this problem for various types of queries including SPJ queries, \Topk queries, group-by aggregate queries, and clust…
Nearest neighbor (NN) queries in trajectory databases have received significant attention in the past, due to their application in spatio-temporal data analysis. Recent work has considered the realistic case where the trajectories are uncertain; however, only simple uncertainty models have been proposed, which do not allow for accurate probabilistic search. In this paper, we fill this gap by addressing probabilistic nearest neighbor queries in databases with uncertain trajectories modeled by stochastic processes, specifically the Markov chain model. We study three nearest neighbor query semant…
This paper presents a query evaluation technique for positive relational algebra queries with aggregates on a representation system for probabilistic data based on the algebraic structures of semiring and semimodule. The core of our evaluation technique is a procedure that compiles semimodule and semiring expressions into so-called decomposition trees, for which the computation of the probability distribution can be done in time linear in the product of the sizes of the probability distributions represented by its nodes. We give syntactic characterisations of tractable queries with aggregates …
We study here fundamental issues involved in top-k query evaluation in probabilistic databases. We consider simple probabilistic databases in which probabilities are associated with individual tuples, and general probabilistic databases in which, additionally, exclusivity relationships between tuples can be represented. In contrast to other recent research in this area, we do not limit ourselves to injective scoring functions. We formulate three intuitive postulates that the semantics of top-k queries in probabilistic databases should satisfy, and introduce a new semantics, Global-Topk, that s…
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）
This paper proposes a new approach for approximate evaluation of #P-hard queries with probabilistic databases. In our approach, every query is evaluated entirely in the database engine by evaluating a fixed number of query plans, each providing an upper bound on the true probability, then taking their minimum. We provide an algorithm that takes into account important schema information to enumerate only the minimal necessary plans among all possible plans. Importantly, this algorithm is a strict generalization of all known results of PTIME self-join-free conjunctive queries: A query is safe if…
We focus on range query processing on large-scale, typically distributed infrastructures, such as clouds of thousands of nodes of shared-datacenters, of p2p distributed overlays, etc. In such distributed environments, efficient range query processing is the key for managing the distributed data sets per se, and for monitoring the infrastructure's resources. We wish to develop an architecture that can support range queries in such large-scale decentralized environments and can scale in terms of the number of nodes as well as in terms of the data items stored. Of course, in the last few years th…
We study the complexity of query answering using views in a probabilistic XML setting, identifying large classes of XPath queries -- with child and descendant navigation and predicates -- for which there are efficient (PTime) algorithms. We consider this problem under the two possible semantics for XML query results: with persistent node identifiers and in their absence. Accordingly, we consider rewritings that can exploit a single view, by means of compensation, and rewritings that can use multiple views, by means of intersection. Since in a probabilistic setting queries return answers with p…
There is a growing realization that uncertain information is a first-class citizen in modern database management. As such, we need techniques to correctly and efficiently process uncertain data in database systems. In particular, data reduction techniques that can produce concise, accurate synopses of large probabilistic relations are crucial. Similar to their deterministic relation counterparts, such compact probabilistic data synopses can form the foundation for human understanding and interactive data exploration, probabilistic query planning and optimization, and fast approximate query pro…
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 tu…
The problem of recovering (count and sum) range queries over multidimensional data only on the basis of aggregate information on such data is addressed. This problem can be formalized as follows. Suppose that a transformation T producing a summary from a multidimensional data set is used. Now, given a data set D, a summary S=T(D) and a range query r on D, the problem consists of studying r by modelling it as a random variable defined over the sample space of all the data sets D' such that T(D) = S. The study of such a random variable, done by the definition of its probability distribution and …
Probabilistic databases play a preeminent role in the processing and management of uncertain data. Recently, many database research efforts have integrated probabilistic models into databases to support tasks such as information extraction and labeling. Many of these efforts are based on batch oriented inference which inhibits a realtime workflow. One important task is entity resolution (ER). ER is the process of determining records (mentions) in a database that correspond to the same real-world entity. Traditional pairwise ER methods can lead to inconsistencies and low accuracy due to localiz…
The Shapley value is a game-theoretic notion for wealth distribution that is nowadays extensively used to explain complex data-intensive computation, for instance, in network analysis or machine learning. Recent theoretical works show that query evaluation over relational databases fits well in this explanation paradigm. Yet, these works fall short of providing practical solutions to the computational challenge inherent to the Shapley computation. We present in this paper two practically effective solutions for computing Shapley values in query answering. We start by establishing a tight theor…
We propose a framework for modeling uncertainty where both belief and doubt can be given independent, first-class status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of information in the form of a confidence level, consisting of a pair of intervals of probability, one for each of her belief and doubt. The space of confidence levels naturally leads to the notion of a trilattice, similar in spirit to Fitting's bilattices. Intuitively, thep oints in such a trilattice can be ordered acc…
Large sparse sets of binary transaction data with millions of records and thousands of attributes occur in various domains: customers purchasing products, users visiting web pages, and documents containing words are just three typical examples. Real-time query selectivity estimation (the problem of estimating the number of rows in the data satisfying a given predicate) is an important practical problem for such databases. We investigate the application of probabilistic models to this problem. In particular, we study a Markov random field (MRF) approach based on frequent sets and maximum entrop…
We consider the problem of exact probabilistic inference for Union of Conjunctive Queries (UCQs) on tuple-independent databases. For this problem, two approaches currently coexist. In the extensional method, query evaluation is performed by exploiting the structure of the query, and relies heavily on the use of the inclusion-exclusion principle. In the intensional method, one first builds a representation of the lineage of the query in a tractable formalism of knowledge compilation. The chosen formalism should then ensure that the probability can be efficiently computed using simple disjointne…
This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful fragment of SQL, namely positive relational algebra with aggregates, whose bag semantics we extend to the partially ordered setting. Our semantics leads to the study of two main computational problems: the possibility and certainty of query answers. We show that these problems are respectively NP-complete and coNP-complete, but identify tractable cases depending o…
Query tractability has been traditionally defined as a function of input database and query sizes, or of both input and output sizes, where the query result is represented as a bag of tuples. In this report, we introduce a framework that allows to investigate tractability beyond this setting. The key insight is that, although the cardinality of a query result can be exponential, its structure can be very regular and thus factorisable into a nested representation whose size is only polynomial in the size of both the input database and query. For a given query result, there may be several equiva…
In many real-world applications such as business planning and sensor data monitoring, one important, yet challenging, the task is to rank objects(e.g., products, documents, or spatial objects) based on their ranking scores and efficiently return those objects with the highest scores. In practice, due to the unreliability of data sources, many real-world objects often contain noises and are thus imprecise and uncertain. In this paper, we study the problem of probabilistic top-k dominating(PTD) query on such large-scale uncertain data in a distributed environment, which retrieves k uncertain obj…
The dramatic growth in the number of application domains that naturally generate probabilistic, uncertain data has resulted in a need for efficiently supporting complex querying and decision-making over such data. In this paper, we present a unified approach to ranking and top-k query processing in probabilistic databases by viewing it as a multi-criteria optimization problem, and by deriving a set of features that capture the key properties of a probabilistic dataset that dictate the ranked result. We contend that a single, specific ranking function may not suffice for probabilistic databases…
The formalism of RPQs (regular path queries) is an important building block of most query languages for graph databases. RPQs are generally evaluated under homomorphism semantics; in particular only the endpoints of the matched walks are returned. Practical applications often need the full matched walks to compute aggregate values. In those cases, homomorphism semantics are not suitable since the number of matched walks can be infinite. Hence, graph-database engines adapt the semantics of RPQs, often neglecting theoretical red flags. For instance, the popular query language Cypher uses trail s…
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）
Probabilistic inference over large data sets is a challenging data management problem since exact inference is generally #P-hard and is most often solved approximately with sampling-based methods today. This paper proposes an alternative approach for approximate evaluation of conjunctive queries with standard relational databases: In our approach, every query is evaluated entirely in the database engine by evaluating a fixed number of query plans, each providing an upper bound on the true probability, then taking their minimum. We provide an algorithm that takes into account important schema i…
Adaptive Probabilistic Skyline Analytics for Mobile Edge-Cloud Systems via State-Aware Deep Reinforcement Learning
National Chung Cheng University（中正大学）；Advanced Institute of Manufacturing with High-tech Innovations (AIM-HI), National Chung Cheng University（中正大学先进制造与高科技创新研究院）
Every database system contains a query optimizer that performs query rewrites. Unfortunately, developing query optimizers remains a highly challenging task. Part of the challenges comes from the intricacies and rich features of query languages, which makes reasoning about rewrite rules difficult. In this paper, we propose a machine-checkable denotational semantics for SQL, the de facto language for relational database, for rigorously validating rewrite rules. Unlike previously proposed semantics that are either non-mechanized or only cover a small amount of SQL language features, our semantics…
With the advancement of technology, the data generated in our lives is getting faster and faster, and the amount of data that various applications need to process becomes extremely huge. Therefore, we need to put more effort into analyzing data and extracting valuable information. Cloud computing used to be a good technology to solve a large number of data analysis problems. However, in the era of the popularity of the Internet of Things (IoT), transmitting sensing data back to the cloud for centralized data analysis will consume a lot of wireless communication and network transmission costs. …
Databases can leak confidential information when users combine query results with probabilistic data dependencies and prior knowledge. Current research offers mechanisms that either handle a limited class of dependencies or lack tractable enforcement algorithms. We propose a foundation for Database Inference Control based on ProbLog, a probabilistic logic programming language. We leverage this foundation to develop Angerona, a provably secure enforcement mechanism that prevents information leakage in the presence of probabilistic dependencies. We then provide a tractable inference algorithm fo…
