126 research outputs found
Shared Arrangements: practical inter-query sharing for streaming dataflows
Current systems for data-parallel, incremental processing and view
maintenance over high-rate streams isolate the execution of independent
queries. This creates unwanted redundancy and overhead in the presence of
concurrent incrementally maintained queries: each query must independently
maintain the same indexed state over the same input streams, and new queries
must build this state from scratch before they can begin to emit their first
results. This paper introduces shared arrangements: indexed views of maintained
state that allow concurrent queries to reuse the same in-memory state without
compromising data-parallel performance and scaling. We implement shared
arrangements in a modern stream processor and show order-of-magnitude
improvements in query response time and resource consumption for interactive
queries against high-throughput streams, while also significantly improving
performance in other domains including business analytics, graph processing,
and program analysis
A simple and practical algorithm for differentially private data release
We present new theoretical results on differentially private data release useful with respect to any target class of counting queries, coupled with experimental results on a variety of real world data sets.
Specifically, we study a simple combination of the multiplicative weights approach of [Hardt and Rothblum, 2010] with the exponential mechanism of [McSherry and Talwar, 2007]. The multiplicative weights framework allows us to maintain and improve a distribution approximating a given data set with respect to a set of counting queries. We use the exponential mechanism to select those queries most incorrectly tracked by the current distribution. Combing the two, we quickly approach a distribution that agrees with the data set on the given set of queries up to small error.
The resulting algorithm and its analysis is simple, but nevertheless improves upon previous work in terms of both error and running time. We also empirically demonstrate the practicality of our approach on several data sets commonly used in the statistical community for contingency table release
Foundations of Differential Dataflow
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 matrix computations for pair-wise and column-wise commute times and Katz scores
We first explore methods for approximating the commute time and Katz score
between a pair of nodes. These methods are based on the approach of matrices,
moments, and quadrature developed in the numerical linear algebra community.
They rely on the Lanczos process and provide upper and lower bounds on an
estimate of the pair-wise scores. We also explore methods to approximate the
commute times and Katz scores from a node to all other nodes in the graph.
Here, our approach for the commute times is based on a variation of the
conjugate gradient algorithm, and it provides an estimate of all the diagonals
of the inverse of a matrix. Our technique for the Katz scores is based on
exploiting an empirical localization property of the Katz matrix. We adopt
algorithms used for personalized PageRank computing to these Katz scores and
theoretically show that this approach is convergent. We evaluate these methods
on 17 real world graphs ranging in size from 1000 to 1,000,000 nodes. Our
results show that our pair-wise commute time method and column-wise Katz
algorithm both have attractive theoretical properties and empirical
performance.Comment: 35 pages, journal version of
http://dx.doi.org/10.1007/978-3-642-18009-5_13 which has been submitted for
publication. Please see
http://www.cs.purdue.edu/homes/dgleich/publications/2011/codes/fast-katz/ for
supplemental code
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