Structure-Aware Sampling: Flexible and Accurate Summarization

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

Efficient Discovery of Association Rules and Frequent Itemsets through Sampling with Tight Performance Guarantees

The tasks of extracting (top-$K$) Frequent Itemsets (FI's) and Association Rules (AR's) are fundamental primitives in data mining and database applications. Exact algorithms for these problems exist and are widely used, but their running time is hindered by the need of scanning the entire dataset, possibly multiple times. High quality approximations of FI's and AR's are sufficient for most practical uses, and a number of recent works explored the application of sampling for fast discovery of approximate solutions to the problems. However, these works do not provide satisfactory performance guarantees on the quality of the approximation, due to the difficulty of bounding the probability of under- or over-sampling any one of an unknown number of frequent itemsets. In this work we circumvent this issue by applying the statistical concept of \emph{Vapnik-Chervonenkis (VC) dimension} to develop a novel technique for providing tight bounds on the sample size that guarantees approximation within user-specified parameters. Our technique applies both to absolute and to relative approximations of (top-$K$) FI's and AR's. The resulting sample size is linearly dependent on the VC-dimension of a range space associated with the dataset to be mined. The main theoretical contribution of this work is a proof that the VC-dimension of this range space is upper bounded by an easy-to-compute characteristic quantity of the dataset which we call \emph{d-index}, and is the maximum integer $d$ such that the dataset contains at least $d$ transactions of length at least $d$ such that no one of them is a superset of or equal to another. We show that this bound is strict for a large class of datasets.Comment: 19 pages, 7 figures. A shorter version of this paper appeared in the proceedings of ECML PKDD 201

QuickSel: Quick Selectivity Learning with Mixture Models

Estimating the selectivity of a query is a key step in almost any cost-based query optimizer. Most of today's databases rely on histograms or samples that are periodically refreshed by re-scanning the data as the underlying data changes. Since frequent scans are costly, these statistics are often stale and lead to poor selectivity estimates. As an alternative to scans, query-driven histograms have been proposed, which refine the histograms based on the actual selectivities of the observed queries. Unfortunately, these approaches are either too costly to use in practice---i.e., require an exponential number of buckets---or quickly lose their advantage as they observe more queries. In this paper, we propose a selectivity learning framework, called QuickSel, which falls into the query-driven paradigm but does not use histograms. Instead, it builds an internal model of the underlying data, which can be refined significantly faster (e.g., only 1.9 milliseconds for 300 queries). This fast refinement allows QuickSel to continuously learn from each query and yield increasingly more accurate selectivity estimates over time. Unlike query-driven histograms, QuickSel relies on a mixture model and a new optimization algorithm for training its model. Our extensive experiments on two real-world datasets confirm that, given the same target accuracy, QuickSel is 34.0x-179.4x faster than state-of-the-art query-driven histograms, including ISOMER and STHoles. Further, given the same space budget, QuickSel is 26.8%-91.8% more accurate than periodically-updated histograms and samples, respectively

Duet: efficient and scalable hybriD neUral rElation undersTanding

Learned cardinality estimation methods have achieved high precision compared to traditional methods. Among learned methods, query-driven approaches face the data and workload drift problem for a long time. Although both query-driven and hybrid methods are proposed to avoid this problem, even the state-of-the-art of them suffer from high training and estimation costs, limited scalability, instability, and long-tailed distribution problem on high cardinality and high-dimensional tables, which seriously affects the practical application of learned cardinality estimators. In this paper, we prove that most of these problems are directly caused by the widely used progressive sampling. We solve this problem by introducing predicates information into the autoregressive model and propose Duet, a stable, efficient, and scalable hybrid method to estimate cardinality directly without sampling or any non-differentiable process, which can not only reduces the inference complexity from O(n) to O(1) compared to Naru and UAE but also achieve higher accuracy on high cardinality and high-dimensional tables. Experimental results show that Duet can achieve all the design goals above and be much more practical and even has a lower inference cost on CPU than that of most learned methods on GPU

Rank-aware, Approximate Query Processing on the Semantic Web

Search over the Semantic Web corpus frequently leads to queries having large result sets. So, in order to discover relevant data elements, users must rely on ranking techniques to sort results according to their relevance. At the same time, applications oftentimes deal with information needs, which do not require complete and exact results. In this thesis, we face the problem of how to process queries over Web data in an approximate and rank-aware fashion

Handling Tradeoffs between Performance and Query-Result Quality in Data Stream Processing

Data streams in the form of potentially unbounded sequences of tuples arise naturally in a large variety of domains including finance markets, sensor networks, social media, and network traffic management. The increasing number of applications that require processing data streams with high throughput and low latency have promoted the development of data stream processing systems (DSPS). A DSPS processes data streams with continuous queries, which are issued once and return query results to users continuously as new tuples arrive. For stream-based applications, both the query-execution performance (in terms of, e.g., throughput and end-to-end latency) and the quality of produced query results (in terms of, e.g., accuracy and completeness) are important. However, a DSPS often needs to make tradeoffs between these two requirements, either because of the data imperfection within the streams, or because of the limited computation capacity of the DSPS itself. Performance versus result-quality tradeoffs caused by data imperfection are inevitable, because the quality of the incoming data is beyond the control of a DSPS, whereas tradeoffs caused by system limitations can be alleviated—even erased—by enhancing the DSPS itself. This dissertation seeks to advance the state of the art on handling the performance versus result-quality tradeoffs in data stream processing caused by the above two aspects of reasons. For tradeoffs caused by data imperfection, this dissertation focuses on the typical data-imperfection problem of stream disorder and proposes the concept of quality-driven disorder handling (QDDH). QDDH enables a DSPS to make flexible and user-configurable tradeoffs between the end-to-end latency and the query-result quality when dealing with stream disorder. Moreover, compared to existing disorder handling approaches, QDDH can significantly reduce the end-to-end latency, and at the same time provide users with desired query-result quality. In this dissertation, a generic buffer-based QDDH framework and three instantiations of the generic framework for distinct query types are presented. For tradeoffs caused by system limitations, this dissertation proposes a system-enhancement approach that combines the row-oriented and the column-oriented data layout and processing techniques in data stream processing to improve the throughput. To fully exploit the potential of such hybrid execution of continuous queries, a static, cost-based query optimizer is introduced. The optimizer works at the operator level and takes the unique property of execution plans of continuous queries—feasibility—into account