Online Lewis Weight Sampling
David P. Woodruff, Taisuke Yasuda

TL;DR
This paper develops nearly optimal online Lewis weight sampling algorithms for all p in (0,∞), enabling efficient subspace embeddings and coresets in streaming models, and introduces new analysis techniques connecting to online linear algebra.
Contribution
It provides the first nearly optimal online algorithms for all p in (0,∞) for Lewis weight sampling and subspace embeddings, extending prior work limited to p=1,2.
Findings
Achieved nearly optimal sample complexity for all p in (0,∞).
First analysis of one-shot Lewis weight sampling with improved bounds.
Developed one-pass streaming coreset algorithms for generalized linear models.
Abstract
The seminal work of Cohen and Peng introduced Lewis weight sampling to the theoretical computer science community, yielding fast row sampling algorithms for approximating -dimensional subspaces of up to error. Several works have extended this important primitive to other settings, including the online coreset and sliding window models. However, these results are only for , and results for require a suboptimal samples. In this work, we design the first nearly optimal subspace embeddings for all in the online coreset and sliding window models. In both models, our algorithms store rows. This answers a substantial generalization of the main open question of [BDMMUWZ2020], and gives the first results for all . Towards our result, we give…
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Taxonomy
TopicsStochastic Gradient Optimization Techniques · Sparse and Compressive Sensing Techniques · Markov Chains and Monte Carlo Methods
MethodsLogistic Regression
