Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Sharper Bounds for $\ell_p$ Sensitivity Sampling
Authors: David Woodruff, Taisuke Yasuda
ICML 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we show the first bounds for sensitivity sampling for βπsubspace embeddings for π = 2 that improve over the general Sπbound, achieving a bound of roughly S2/πfor 1 π< 2 and S2 2/πfor 2 < π< . For 1 π< 2, we show that this bound is tight, in the sense that there exist matrices for which S2/πsamples is necessary. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly πfor 1 π< 2, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly π2/πS2 4/πfor 2 < π< . Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small βπsensitivity. ... Our work introduces a new analysis for sensitivity sampling for βπsubspace embeddings, which breaks a previous general sampling barrier of π(π 2Sπ(A)π) samples via a simple union bound argument, to obtain an improved bound of π(π 2Sπ(A)2/π) samples for π< 2 and π(π 2Sπ(A)2 2/π) samples for π> 2. |
| Researcher Affiliation | Academia | 1Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, US. Correspondence to: Taisuke Yasuda <EMAIL>. |
| Pseudocode | No | The paper describes algorithmic procedures in prose but does not include any explicitly labeled 'Pseudocode' or 'Algorithm' blocks. |
| Open Source Code | No | The paper does not contain any statement about releasing source code for the described methodology, nor does it provide any links to a code repository. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments on a specific dataset, therefore no public dataset access information is provided. |
| Dataset Splits | No | The paper is theoretical and does not describe empirical experiments or data processing, thus no training/test/validation dataset splits are provided. |
| Hardware Specification | No | The paper is theoretical and does not describe empirical experiments, therefore no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe empirical experiments, therefore no software dependencies with version numbers are listed. |
| Experiment Setup | No | The paper is theoretical and does not describe empirical experiments, therefore no specific experimental setup details or hyperparameters are provided. |