On the Sampling Problem for Kernel Quadrature
Authors: François-Xavier Briol, Chris J. Oates, Jon Cockayne, Wilson Ye Chen, Mark Girolami
ICML 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirical results demonstrate a dramatic reduction in integration error of up to 4 orders of magnitude can be achieved with the proposed method. (Abstract) and Numerical experiments, presented in Sec. 4, demonstrate that dramatic reductions in integration error (up to 4 orders of magnitude) can be achieved with SMC-KQ. (Section 1) and Here we compared SMC-KQ (and SMC-KQ-KL) against the corresponding default approaches KQ (and KQ-KL)... Sec. 4.1 below reports an assessment in which the true value of integrals is known by design, while in Sec. 4.2 the methods were deployed to solve a parameter estimation problem involving differential equations. (Section 4) |
| Researcher Affiliation | Academia | 1University of Warwick, Department of Statistics. 2Imperial College London, Department of Mathematics. 3Newcastle University, School of Mathematics and Statistics 4The Alan Turing Institute for Data Science 5University of Technology Sydney, School of Mathematical and Physical Sciences. |
| Pseudocode | Yes | Full pseudo-code for SMC-KQ is provided as Alg. 1, while SMC-KQ-KL is Alg. 9 in the Appendix. (Section 3.5) and pseudo-code is provided as Alg. 2 in the Appendix. (Section 3.2) |
| Open Source Code | No | No explicit statement or link indicating the release of source code for the methodology described in the paper. |
| Open Datasets | No | The paper uses synthetic problems (e.g., 'f(x) = 1 + sin(2πx)' with 'Π = N(0, 1)' and 'Hooke’s law' for differential equations) which are not publicly available datasets in the conventional sense (no links, DOIs, or citations to established dataset repositories). |
| Dataset Splits | No | No specific details on training, validation, or test dataset splits (e.g., percentages, sample counts, or references to predefined splits) are provided in the paper. |
| Hardware Specification | No | No specific hardware details (e.g., CPU/GPU models, memory specifications, or cloud instance types) used for running the experiments are mentioned in the paper. |
| Software Dependencies | No | No specific software dependencies with version numbers are provided (e.g., 'Python 3.8, PyTorch 1.9'). |
| Experiment Setup | Yes | All experiments employed SMC with N = 300 particles, random walk Metropolis transitions (Alg. 3), the re-sample threshold ρ = 0.95 and a maximum grid size = 0.1. (Section 4.1) and For the SMC algorithm, an independent log-normal transition kernel was used at each iteration with parameters automatically tuned to the current set of particles. (Section 4.2) |