Kernel Quadrature with Randomly Pivoted Cholesky
Authors: Ethan Epperly, Elvira Moreno
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | 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 {eepperly,emoreno2}@caltech.edu |
| 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. |