On Average-Case Error Bounds for Kernel-Based Bayesian Quadrature
Authors: Xu Cai, Thanh Lam, Jonathan Scarlett
TMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we conduct simulation studies to compare our two-batch algorithm with its component parts, maximum variance sampling (MVS) and Monte Carlo sampling (MC). These experiments serve to verify that Algorithm 1 can be effective in practice, but we will also discuss some potential gaps between the theory and practice. We let MVS and MVS-MC know the kernel hyperparameters exactly (i.e., they match the ones used to produce the functions). Some results for d = 3 and σ {0.1, 0.5} are shown in Figure 1, and further (d, σ) pairs are shown in Appendix G. |
| Researcher Affiliation | Academia | Xu Cai EMAIL Department of Computer Science National University of Singapore Chi Thanh Lam EMAIL Department of Computer Science National University of Singapore Jonathan Scarlett EMAIL Department of Computer Science, Department of Mathematics, Institute of Data Science National University of Singapore |
| Pseudocode | Yes | Algorithm 1 Two-batch integral estimation meta-algorithm |
| Open Source Code | Yes | The code can be found at https://github.com/caitree/Kernelized-Bayesian-Quadrature. |
| Open Datasets | Yes | We consider a variety of well-known benchmark functions, namely, Ackley, Alpine, Gramacy-Lee, Griewank and Keane; see (Bingham, 2013) for the descriptions. ... The data set consists of energy consumption readings for London Households that took part in the UK Power Networks led Low Carbon London Project, between November 2011 and February 2014.8 ... 8The data can be downloaded at data.london.gov.uk. |
| Dataset Splits | No | The paper does not provide specific training/test/validation dataset splits. It describes generating synthetic functions and using benchmark functions, with evaluation over a time horizon, but not data splitting for model evaluation. |
| Hardware Specification | No | The paper does not provide any specific hardware details used for running its experiments. |
| Software Dependencies | No | The paper mentions using 'the built-in Sci Py optimizer based on L-BFGS-B' but does not provide specific version numbers for SciPy or any other software libraries. |
| Experiment Setup | Yes | We adopt the common choice ν = 3/2 for Matérn-ν kernel, and the GP mean noise hyperparameter λµ is fixed as 10 5 for both kernels 6. The lengthscale is left as a free parameter, as is an additional scale parameter that we introduce (multiplying (2)) to permit functions with varying ranges. ... For all functions, we consider a time horizon of T = 250 |