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..
Is Input Sparsity Time Possible for Kernel Low-Rank Approximation?
Authors: Cameron Musco, David Woodruff
NeurIPS 2017 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We show that for a broad class of kernels, including the popular Gaussian and polynomial kernels, computing a relative error k-rank approximation to K is at least as difficult as multiplying the input data matrix A 2 Rn d by an arbitrary matrix C 2 Rd k. Barring a breakthrough in fast matrix multiplication, when k is not too large, this requires (nnz(A)k) time where nnz(A) is the number of non-zeros in A. This lower bound matches, in many parameter regimes, recent work on subquadratic time algorithms for low-rank approximation of general kernels [MM16, MW17], demonstrating that these algorithms are unlikely to be significantly improved, in particular to O(nnz(A)) input sparsity runtimes. At the same time there is hope: we show for the first time that O(nnz(A)) time approximation is possible for general radial basis function kernels (e.g., the Gaussian kernel) for the closely related problem of low-rank approximation of the kernelized dataset. |
| Researcher Affiliation | Academia | Cameron Musco MIT EMAIL David P. Woodruff Carnegie Mellon University EMAIL |
| Pseudocode | No | No pseudocode or algorithm blocks were found. |
| Open Source Code | No | The paper does not provide any statement or link for open-source code specific to the methodology described. |
| Open Datasets | No | This is a theoretical paper that does not involve empirical evaluation with datasets. Therefore, no information about public dataset availability is provided. |
| Dataset Splits | No | This is a theoretical paper and does not discuss dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe experimental hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not describe software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not provide details on experimental setup or hyperparameters. |