1,827 research outputs found

    Deterministic Sampling and Range Counting in Geometric Data Streams

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    We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.Comment: 12 pages, 1 figur

    Differentially Private Publication of Sparse Data

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    The problem of privately releasing data is to provide a version of a dataset without revealing sensitive information about the individuals who contribute to the data. The model of differential privacy allows such private release while providing strong guarantees on the output. A basic mechanism achieves differential privacy by adding noise to the frequency counts in the contingency tables (or, a subset of the count data cube) derived from the dataset. However, when the dataset is sparse in its underlying space, as is the case for most multi-attribute relations, then the effect of adding noise is to vastly increase the size of the published data: it implicitly creates a huge number of dummy data points to mask the true data, making it almost impossible to work with. We present techniques to overcome this roadblock and allow efficient private release of sparse data, while maintaining the guarantees of differential privacy. Our approach is to release a compact summary of the noisy data. Generating the noisy data and then summarizing it would still be very costly, so we show how to shortcut this step, and instead directly generate the summary from the input data, without materializing the vast intermediate noisy data. We instantiate this outline for a variety of sampling and filtering methods, and show how to use the resulting summary for approximate, private, query answering. Our experimental study shows that this is an effective, practical solution, with comparable and occasionally improved utility over the costly materialization approach

    Towards Optimal Multi-Dimensional Query Processing with BitmapIndices

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    Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting

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    Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic guarantees are obtained in O(nm), where n denotes the number of variables, and m the number of clauses of the input DNF, but this is not scalable in practice. In this paper, we propose a neural model counting approach for weighted #DNF that combines approximate model counting with deep learning, and accurately approximates model counts in linear time when width is bounded. We conduct experiments to validate our method, and show that our model learns and generalizes very well to large-scale #DNF instances.Comment: To appear in Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20). Code and data available at: https://github.com/ralphabb/NeuralDNF

    ProS: Data Series Progressive k-NN Similarity Search and Classification with Probabilistic Quality Guarantees

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    Existing systems dealing with the increasing volume of data series cannot guarantee interactive response times, even for fundamental tasks such as similarity search. Therefore, it is necessary to develop analytic approaches that support exploration and decision making by providing progressive results, before the final and exact ones have been computed. Prior works lack both efficiency and accuracy when applied to large-scale data series collections. We present and experimentally evaluate ProS, a new probabilistic learning-based method that provides quality guarantees for progressive Nearest Neighbor (NN) query answering. We develop our method for k-NN queries and demonstrate how it can be applied with the two most popular distance measures, namely, Euclidean and Dynamic Time Warping (DTW). We provide both initial and progressive estimates of the final answer that are getting better during the similarity search, as well suitable stopping criteria for the progressive queries. Moreover, we describe how this method can be used in order to develop a progressive algorithm for data series classification (based on a k-NN classifier), and we additionally propose a method designed specifically for the classification task. Experiments with several and diverse synthetic and real datasets demonstrate that our prediction methods constitute the first practical solutions to the problem, significantly outperforming competing approaches. This paper was published in the VLDB Journal (2022)
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