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..
Kernel Quadrature with Randomly Pivoted Cholesky
Authors: Ethan Epperly, Elvira Moreno
NeurIPS 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Theoretical and numerical results show that randomly pivoted Cholesky is fast and achieves comparable quadrature error rates to more computationally expensive quadrature schemes... The quadrature error for f(x, y) = sin(x) exp(y), g 1, and different numbers n of quadrature nodes for RPCHOLESKY kernel quadrature, kernel quadrature with nodes drawn iid from µ/µ(X), and Monte Carlo quadrature are shown in fig. 1b. ... Errors for the different methods are shown in fig. 2 (left panels). ... Results are shown in fig. 3. |
| Researcher Affiliation | Academia | Ethan N. Epperly and Elvira Moreno Department of Computing and Mathematical Sciences California Institute of Technology Pasadena, CA 91125 EMAIL |
| Pseudocode | Yes | Algorithm 1 RPCHOLESKY: unoptimized implementation. Algorithm 2 RPCHOLESKY with rejection sampling. Algorithm 3 Helper subroutine to evaluate residual kernel. Algorithm 4 RPCHOLESKY with optimized rejection sampling. |
| Open Source Code | Yes | Our code is available at https://github.com/eepperly/RPCholesky-Kernel-Quadrature. |
| Open Datasets | Yes | For X, we use 2 104 randomly selected points from the QM9 dataset [33, 37, 40]. |
| Dataset Splits | No | The paper describes the methods and how performance is quantified using `Err(S, w; g)` but does not provide specific train/validation/test dataset splits or methodologies for creating them. |
| Hardware Specification | Yes | Experiments were run on a Mac Book Pro with a 2.4 GHz 8-Core Intel Core i9 CPU and 64 GB 2667 MHz DDR4 RAM. |
| Software Dependencies | No | The paper mentions software like Cheb Fun, goodpoints package, and DScribe package, but does not provide specific version numbers for these dependencies. |
| Experiment Setup | Yes | In our experiments, we initialize with s1, . . . , sn drawn iid from µ and run for 10n MCMC steps. We use g = 4, δ = 0.5, and four bins for the COMPRESS++ algorithm. To compute the optimal weights (8), we add a small multiple of the identity to regularize the system: w , reg = (k(S, S) + 10εmach trace(k(S, S)) I) 1Tg(S). Here, εmach = 2 52 is the double precision machine epsilon. |