1,458 research outputs found
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 Differentially Private Matrix Factorization
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
Redacted by arXiv.Comment: This article has been removed by arXiv due a copyright claim by a 3rd
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A Differential Datalog Interpreter
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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