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..
Entrywise error bounds for low-rank approximations of kernel matrices
Authors: Alexander Modell
NeurIPS 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we validate our theory with an empirical study of a collection of synthetic and real-world datasets. |
| Researcher Affiliation | Academia | Alexander Modell Department of Mathematics Imperial College London, U.K. EMAIL |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. It focuses on theoretical derivations and proofs. |
| Open Source Code | Yes | Code to reproduce the experiments in this section can be found at https://gist.github.com/alexandermodell/b16b0b29b6d0a340a23dab79219133f2. |
| Open Datasets | Yes | GMM is a synthetic dataset... Abalone [Nash et al., 1995]... Wine Quality [Cortez et al., 2009]... MNIST [Deng, 2012]... 20 Newsgroups [Lang, 1995]... Zebrafish [Wagner et al., 2018]. |
| Dataset Splits | No | The paper does not explicitly provide training/test/validation dataset splits. It mentions that some datasets are |
| Hardware Specification | Yes | The experiments were performed on the HPC cluster at Imperial College London with 8 cores and 16GB of RAM. |
| Software Dependencies | No | The paper mentions using 'the svds function in the SciPy library for Python [Virtanen et al., 2020]' but does not provide specific version numbers for Python or SciPy. |
| Experiment Setup | Yes | For each dataset, we construct four kernel matrices using Matรฉrn kernels with smoothness parameters ฮฝ = 1/2, 3/2, 5/2, โ, each time selecting the bandwidth using the median heuristic. For each kernel, we compute the best rank-d low-rank approximation of the kernel matrix using the svds function in the SciPy library for Python [Virtanen et al., 2020]. We do this for a range of ranks d from 1 to n, where n is the number of instances in the dataset, and record the entrywise errors. |