arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1902.03498cs.LGstat.ML
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流模型中线性预测的空间下界

Space lower bounds for linear prediction in the streaming model

Massachusetts Institute of Technology(麻省理工学院);Weizmann Institute of Science(魏茨曼科学研究所)

Yuval Dagan, Gil Kur, Ohad Shamir

摘要:

我们发现,基本的学习任务,如找到一个近似的线性分离器或线性回归,需要内存至少\emph{quadratic}的尺寸,在一个自然的流设置。这意味着这样的问题不能解决(至少在这种情况下)可扩展的内存高效流算法。我们的研究结果建立在一个简单的线性代数问题的记忆下限-找到正交向量-并利用包装的格拉斯曼,固定尺寸的所有线性子空间的流形上的估计。

英文摘要:

We show that fundamental learning tasks, such as finding an approximate linear separator or linear regression, require memory at least \emph{quadratic} in the dimension, in a natural streaming setting. This implies that such problems cannot be solved (at least in this setting) by scalable memory-efficient streaming algorithms. Our results build on a memory lower bound for a simple linear-algebraic problem -- finding orthogonal vectors -- and utilize the estimates on the packing of the Grassmannian, the manifold of all linear subspaces of fixed dimension.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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