Approximate Query Answering Research Articles

On Efficient Approximate Queries over Machine Learning Models

The question of answering queries over ML predictions has been gaining attention in the database community. This question is challenging because finding high quality answers by invoking an oracle such as a human expert or an expensive deep neural network model on every single item in the DB and then applying the query, can be prohibitive. We develop a novel unified framework for approximate query answering by leveraging a proxy to minimize the oracle usage of finding high quality answers for both Precision-Target (PT) and Recall-Target (RT) queries. Our framework uses a judicious combination of invoking the expensive oracle on data samples and applying the cheap proxy on the DB objects. It relies on two assumptions. Under the P roxy Q uality assumption, we develop two algorithms: PQA that efficiently finds high quality answers with high probability and no oracle calls, and PQE, a heuristic extension that achieves empirically good performance with a small number of oracle calls. Alternatively, under the C ore S et C losure assumption, we develop two algorithms: CSC that efficiently returns high quality answers with high probability and minimal oracle usage, and CSE, which extends it to more general settings. Our extensive experiments on five real-world datasets on both query types, PT and RT, demonstrate that our algorithms outperform the state-of-the-art and achieve high result quality with provable statistical guarantees.

Approximate Query Answering Based on Topological Neighborhood and Semantic Similarity in OpenStreetMap

In this paper we focus on a pictorial query language, referred to as Geographical Pictorial Query Language (GeoPQL), and we revise its formal semantics by considering the polygon-polyline, polyline-polyline, and polygon-polygon topological relationships. This work proposes the Approximate Answering Engine (AAE) within a Distributed System, referred to as GeoPQLJSON (GeoPQLJ). The AAE provides approximate answers to query with empty results by following two directions: the Operator Conceptual Neighborhood (OCN) graph, and the OpenStreetMap (OSM) attribute hierarchy, giving maximum flexibility to the user choices. According to the former, the geo-operators of the queries can be replaced with the ones labeling the adjacent nodes of the OCN graph. By following the latter, the system evaluates the OSM attribute semantic similarity according to the information content approach, and proposes possible attribute replacements to the user. Note that the presence of OSM attributes allows the quick and direct access to large amount of geographical data, without requiring in our case the use of the topological elements. The functionalities of the Distributed GeoPQLJ System are illustrated by several query examples.

EntropyDB: a probabilistic approach to approximate query processing

We present, 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 time, and explore methods to reduce query error. Lastly, we experimentally evaluate our work using a 5 GB dataset of flights within the USA and a 210 GB dataset from an astronomy particle simulation. While our current work only supports linear queries, we show that our technique can successfully answer queries faster than sampling while introducing, on average, no more error than sampling and can better distinguish between rare and nonexistent values. We also discuss extensions that can allow for data updates and linear queries over joins.

Improved selectivity estimation by combining knowledge from sampling and synopses

Estimating selectivities remains a critical task in query processing. Optimizers rely on the accuracy of selectivities when generating execution plans and, in approximate query answering, estimated selectivities affect the quality of the result. Many systems maintain synopses, e.g., histograms, and, in addition, provide sampling facilities. In this paper, we present a novel approach to combine knowledge from synopses and sampling for the purpose of selectivity estimation for conjunctive queries. We first show how to extract information from synopses and sampling such that they are mutually consistent. In a second step, we show how to combine them and decide on an admissible selectivity estimate. We compare our approach to state-of-the-art methods and evaluate the strengths and limitations of each approach.

Privacy-Preserving Location Sharing Services for Social Networks

A common functionality of many location-based social networking applications is a location sharing service that allows a group of friends to share their locations. With a potentially untrusted server, such a location sharing service may threaten the privacy of users. Existing solutions for Privacy-Preserving Location Sharing Services (PPLSS) require a trusted third party that has access to the exact location of all users in the system or rely on expensive algorithms or protocols in terms of computational or communication overhead. Other solutions can only provide approximate query answers. To overcome these limitations, we propose a new encryption notion, called Order-Retrievable Encryption (ORE), for PPLSS for social networking applications. The distinguishing characteristics of our PPLSS are that it (1) allows a group of friends to share their exact locations without the need of any third party or leaking any location information to any server or users outside the group, (2) achieves low computational and communication cost by allowing users to receive the exact location of their friends without requiring any direct communication between users or multiple rounds of communication between a user and a server, (3) provides efficient query processing by designing an index structure for our ORE scheme, (4) supports dynamic location updates, and (5) provides personalized privacy protection within a group of friends by specifying a maximum distance where a user is willing to be located by his/her friends. Experimental results show that the computational and communication cost of our PPLSS is much better than the state-of-the-art solution.

Probabilistic database summarization for interactive data exploration

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 experimentally evaluate our work using a 5 GB dataset of flights within the United States and a 210 GB dataset from an astronomy particle simulation. While our current work only supports linear queries, we show that our technique can successfully answer queries faster than sampling while introducing, on average, no more error than sampling and can better distinguish between rare and nonexistent values.

How Progressive Visualizations Affect Exploratory Analysis.

The stated goal for visual data exploration is to operate at a rate that matches the pace of human data analysts, but the ever increasing amount of data has led to a fundamental problem: datasets are often too large to process within interactive time frames. Progressive analytics and visualizations have been proposed as potential solutions to this issue. By processing data incrementally in small chunks, progressive systems provide approximate query answers at interactive speeds that are then refined over time with increasing precision. We study how progressive visualizations affect users in exploratory settings in an experiment where we capture user behavior and knowledge discovery through interaction logs and think-aloud protocols. Our experiment includes three visualization conditions and different simulated dataset sizes. The visualization conditions are: (1) blocking, where results are displayed only after the entire dataset has been processed; (2) instantaneous, a hypothetical condition where results are shown almost immediately; and (3) progressive, where approximate results are displayed quickly and then refined over time. We analyze the data collected in our experiment and observe that users perform equally well with either instantaneous or progressive visualizations in key metrics, such as insight discovery rates and dataset coverage, while blocking visualizations have detrimental effects.

System Architecture for Approximate Query Processing

<p><span style="font-size: 10.5pt; font-family: 'Times New Roman','serif'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US"><span style="font-size: 10.5pt; font-family: 'Times New Roman','serif'; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">Decision making is an activity that addresses the problem of extracting knowledge and information from data stored in data warehouses, in order to improve the business processes of information systems. Usually, decision making is based on On-Line Analytical Processing, data mining, or approximate query processing. In the last case, answers to analytical queries are provided in a fast manner, although affected with a small percentage of error. In the paper, we present the architecture of an approximate query answering system. Then, we illustrate our ADAP (Analytical Data Profile) system, which is based on an engine able to provide fast responses to the main statistical functions by using orthogonal polynomials series to approximate the data distribution of multi­dimensional relations. Moreover, several experimental results to measure the approximation error are shown and the response-time to analytical queries is reported.</span></span></p>

Benchmark for Approximate Query Answering Systems

The standard benchmark for Decision Support Systems is TPC-H, which is composed of a database, a workload, and a set of metrics for the performance evaluation. However, TPC-H does not include a methodology for the benchmark of Approximate Query Answering Systems, or the software tools used to obtain fast answers to analytical queries in the decision making process. In the paper, the authors present a methodology to evaluate and compare Approximate Query Answering Systems. To this aim, a methodology that extends the standard TPC-H and a set of new metrics that take into account the specific features of these systems are proposed. Experimental results show the application of these metrics to two systems based on the data analytic approximation by orthonormal series.

Querying Big Data: Bridging Theory and Practice

Big data introduces challenges to query answering, from theory to practice. A number of questions arise. What queries are "tractable" on big data? How can we make big data "small" so that it is feasible to find exact query answers? When exact answers are beyond reach in practice, what approximation theory can help us strike a balance between the quality of approximate query answers and the costs of computing such answers? To get sensible query answers in big data, what else do we necessarily do in addition to coping with the size of the data? This position paper aims to provide an overview of recent advances in the study of querying big data. We propose approaches to tackling these challenging issues, and identify open problems for future research.

Theoretical analysis of constructing wavelet synopsis on partitioned data sets

Currently, the size of data becomes much larger and the distributed data processing is getting very important to manage the huge size of data. The MapReduce well known as Google's data processing environment is the most popular distributed platform with good scalability and fault tolerance. Many traditional algorithms in the single machine environment are being adopted to the MapReduce platform. In this paper we analyze a novel algorithm to generate wavelet synopses on the distributed MapReduce framework. Wavelet synopsis is one of the most popular dimensionality reduction methods and has been studied in various areas such as query optimization, approximate query answering, feature selection, etc. In the proposed algorithm, the wavelet synopsis can be calculated by a single MapReduce phase, and, by minimizing the amount of data communicated through the network of the distributed MapReduce platform, all computations are processed within almost linear time complexity. We theoretically study the properties of constructing wavelet synopsis on partitioned data sets and the correctness of the proposed algorithm.

Constraint Propagation for First-Order Logic and Inductive Definitions

In Constraint Programming, constraint propagation is a basic component of constraint satisfaction solvers. Here we study constraint propagation as a basic form of inference in the context of first-order logic (FO) and extensions with inductive definitions (FO(ID)) and aggregates (FO(AGG)). In a first, semantic approach, a theory of propagators and constraint propagation is developed for theories in the context of three-valued interpretations. We present an algorithm with polynomial-time data complexity. We show that constraint propagation in this manner can be represented by a datalog program. In a second, symbolic approach, the semantic algorithm is lifted to a constraint propagation algorithm in symbolic structures , symbolic representations of classes of structures. The third part of the article is an overview of existing and potential applications of constraint propagation for model generation, grounding, interactive search problems, approximate methods for ∃∀SO problems, and approximate query answering in incomplete databases.

Metadata for Approximate Query Answering Systems

In business intelligence systems, data warehouse metadata management and representation are getting more and more attention by vendors and designers. The standard language for the data warehouse metadata representation is the Common Warehouse Metamodel. However, business intelligence systems include also approximate query answering systems, since these software tools provide fast responses for decision making on the basis of approximate query processing. Currently, the standard meta-model does not allow to represent the metadata needed by approximate query answering systems. In this paper, we propose an extension of the standard metamodel, in order to define the metadata to be used in online approximate analytical processing. These metadata have been successfully adopted in ADAP, a web-based approximate query answering system that creates and uses statistical data profiles.

Continuous sampling from distributed streams

A fundamental problem in data management is to draw and maintain a sample of a large data set, for approximate query answering, selectivity estimation, and query planning. With large, streaming data sets, this problem becomes particularly difficult when the data is shared across multiple distributed sites. The main challenge is to ensure that a sample is drawn uniformly across the union of the data while minimizing the communication needed to run the protocol on the evolving data. At the same time, it is also necessary to make the protocol lightweight, by keeping the space and time costs low for each participant. In this article, we present communication-efficient protocols for continuously maintaining a sample (both with and without replacement) from k distributed streams. These apply to the case when we want a sample from the full streams, and to the sliding window cases of only the W most recent elements, or arrivals within the last w time units. We show that our protocols are optimal (up to logarithmic factors), not just in terms of the communication used, but also the time and space costs for each participant.

XPath Query Relaxation through Rewriting Rules

Query relaxation is the process of weakening a query to a more general one, and it is frequently employed to support approximate query answering. In this paper, rewriting systems for a wide fragment of XPath are investigated, which accomplish query relaxation through the application of simple rewriting rules transforming navigational axes and node tests into relaxed ones. Specifically, a general yet simple form of rewriting rules is considered, which subsumes the forms adopted in several rewriting systems for approximate XPath query answering. The expressiveness of rewriting systems based on this form of rules is characterized in terms of their capability of transforming a query into every more general formulation. It is shown that traditional rewriting systems are not only incomplete w.r.t. containment, but also w.r.t. the stricter form known as containment by homomorphism. This limitation is overcome by defining a set R* of rewriting rules which are still of the same simple form of traditional ones, but are expressive enough to catch at least containment by homomorphism. Then, an algorithm is proposed which exploits R* to provide approximate answers of queries along with a measure of their approximation degree.

Structure-aware sampling

In processing large quantities of data, a fundamental problem is to obtain a summary which supports approximate query answering. Random sampling yields flexible summaries which naturally support subset-sum queries with unbiased estimators and well-understood confidence bounds. Classic sample-based summaries, however, are designed for arbitrary subset queries and are oblivious to the structure in the set of keys. The particular structure, such as hierarchy, order, or product space (multi-dimensional), makes range queries much more relevant for most analysis of the data. Dedicated summarization algorithms for range-sum queries have also been extensively studied. They can outperform existing sampling schemes in terms of accuracy on range queries per summary size. Their accuracy, however, rapidly degrades when, as is often the case, the query spans multiple ranges. They are also less flexible---being targeted for range sum queries alone---and are often quite costly to build and use. In this paper we propose and evaluate variance optimal sampling schemes that are structure-aware. These summaries improve over the accuracy of existing structure-oblivious sampling schemes on range queries while retaining the benefits of sample-based summaries: flexible summaries, with high accuracy on both range queries and arbitrary subset queries.

A Bayesian method for query approximation

This study presents statistical techniques to obtain local approximate query answers for aggregate multivariate materialized views thus eliminating the need for repetitive scanning of the source data. In widely distributed management information systems, detailed data do not necessarily reside in the same physical location as the decision-maker; thus, requiring scanning of the source data as needed by the query demand. Decision-making, business intelligence and data analysis could involve multiple data sources, data diversity, aggregates and large amounts of data. Management often confronts delays in information acquisition from remote sites. Management decisions usually involve analyses that require the most precise summary data available. These summaries are readily available from data warehouses and can be used to estimate or approximate data in exchange for a quicker response. An approach to supporting aggregate materialized view management is proposed that reconstructs data sets locally using posterior parameter estimates based on sufficient statistics in a log-linear model with a multinomial likelihood.

Supporting ranking queries on uncertain and incomplete data

Large databases with uncertain information are becoming more common in many applications including data integration, location tracking, and Web search. In these applications, ranking records with uncertain attributes introduces new problems that are fundamentally different from conventional ranking. Specifically, uncertainty in records' scores induces a partial order over records, as opposed to the total order that is assumed in the conventional ranking settings. In this paper, we present a new probabilistic model, based on partial orders, to encapsulate the space of possible rankings originating from score uncertainty. Under this model, we formulate several ranking query types with different semantics. We describe and analyze a set of efficient query evaluation algorithms. We show that our techniques can be used to solve the problem of rank aggregation in partial orders under two widely adopted distance metrics. In addition, we design sampling techniques based on Markov chains to compute approximate query answers. Our experimental evaluation uses both real and synthetic data. The experimental study demonstrates the efficiency and effectiveness of our techniques under various configurations.

Probabilistic histograms for probabilistic data

There is a growing realization that modern database management systems (DBMSs) must be able to manage data that contains uncertainties that are represented in the form of probabilistic relations. Consequently, the design of each core DBMS component must be revisited in the presence of uncertain and probabilistic information. In this paper, we study how to build histogram synopses for probabilistic relations, for the purposes of enabling both DBMS-internal decisions (such as indexing and query planning), and (possibly, user-facing) approximate query processing tools. In contrast to initial work in this area, our probabilistic histograms retain the key possible-worlds semantics of probabilistic data, allowing for more accurate, yet concise, representation of the uncertainty characteristics of data and query results. We present a variety of techniques for building optimal probabilistic histograms, each one tuned to a different choice of approximation-error metric. We show that these can be incorporated into a general Dynamic Programming (DP) framework, which generalizes that used for existing histogram constructions. The end result is a histogram where each "bucket" is approximately represented by a compact probability distribution function (PDF), which can be used as the basis for query planning and approximate query answering. We present novel, polynomial-time algorithms to find optimal probabilistic histograms for a variety of PDF-error metrics (including variation distance, sum squared error, max error and EMD 1 ). Our experimental study shows that our probabilistic histogram synopses can accurately capture the key statistical properties of uncertain data, while being much more compact to store and work with than the original uncertain relations.

AMID: Approximation of MultI-measured Data using SVD

Approximate query answering has recently emerged as an effective method for generating a viable answer. Among various techniques for approximate query answering, wavelets have received a lot of attention. However, wavelet techniques minimizing the root squared error (i.e., the L 2 norm error) have several problems such as the poor quality of reconstructed data when the original data is biased. In this paper, we present AMID ( Approximation of MultI-measured Data using SVD) for multi-measured data. In AMID, we adapt the singular value decomposition (SVD) to compress multi-measured data. We show that SVD guarantees the root squared error, and also drive an error bound of SVD for an individual data value, using mathematical analyses. In addition, in order to improve the accuracy of approximated data, we combine SVD and wavelets in AMID. Since SVD is applied to a fixed matrix, we use various properties of matrices to adapt SVD to the incremental update environment. We devise two variants of AMID for the incremental update environment: incremental AMID and local AMID. To the best of our knowledge, our work is the first to extend SVD to incremental update environments.