1,458 research outputs found

    Foundations of Differential Dataflow

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    Abstract. Differential dataflow is a recent approach to incremental computation that relies on a partially ordered set of differences. In the present paper, we aim to develop its foundations. We define a small pro-gramming language whose types are abelian groups equipped with linear inverses, and provide both a standard and a differential denotational se-mantics. The two semantics coincide in that the differential semantics is the differential of the standard one. Möbius inversion, a well-known idea from combinatorics, permits a systematic treatment of various operators and constructs.

    Fast Differentially Private Matrix Factorization

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    Differentially private collaborative filtering is a challenging task, both in terms of accuracy and speed. We present a simple algorithm that is provably differentially private, while offering good performance, using a novel connection of differential privacy to Bayesian posterior sampling via Stochastic Gradient Langevin Dynamics. Due to its simplicity the algorithm lends itself to efficient implementation. By careful systems design and by exploiting the power law behavior of the data to maximize CPU cache bandwidth we are able to generate 1024 dimensional models at a rate of 8.5 million recommendations per second on a single PC

    Redacted by arXiv

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    Redacted by arXiv.Comment: This article has been removed by arXiv due a copyright claim by a 3rd part

    A Differential Datalog Interpreter

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    The core reasoning task for datalog engines is materialization, the evaluation of a datalog program over a database alongside its physical incorporation into the database itself. The de-facto method of computing it, is through the recursive application of inference rules. Due to it being a costly operation, it is a must for datalog engines to provide incremental materialization, that is, to adjust the computation to new data, instead of restarting from scratch. One of the major caveats, is that deleting data is notoriously more involved than adding, since one has to take into account all possible data that has been entailed from what is being deleted. Differential Dataflow is a computational model that provides efficient incremental maintenance, notoriously with equal performance between additions and deletions, and work distribution, of iterative dataflows. In this paper we investigate the performance of materialization with three reference datalog implementations, out of which one is built on top of a lightweight relational engine, and the two others are differential-dataflow and non-differential versions of the same rewrite algorithm, with the same optimizations
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