A Bayes-Sard Cubature Method
Authors: Toni Karvonen, Chris J. Oates, Simo Sarkka
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The asymptotic convergence of the Bayes Sard cubature method is established and the theoretical results are numerically verified. In particular, we report two orders of magnitude reduction in error compared to Bayesian cubature in the context of a high-dimensional financial integral. This section contains three numerical experiments, which investigate the empirical performance of the BSC method and the associated uncertainty quantification that is provided. |
| Researcher Affiliation | Academia | Toni Karvonen Aalto University, Finland toni.karvonen@aalto.fi Chris. J. Oates Newcastle University, UK Alan Turing Institute, UK chris.oates@ncl.ac.uk Simo Särkkä Aalto University, Finland simo.sarkka@aalto.fi |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link indicating the release of open-source code for the described methodology. |
| Open Datasets | No | The paper evaluates numerical integration methods on mathematical functions and integrals, not on publicly available datasets for which access information is provided. |
| Dataset Splits | No | The paper discusses placing 'nodes' for integration rules (e.g., 'n nodes were placed uniformly'), which are akin to sampling points for numerical integration, but it does not describe training, validation, or test splits of a traditional dataset. |
| Hardware Specification | No | The paper mentions 'computer codes' but does not specify any hardware details like GPU/CPU models, processors, or memory used for experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers (e.g., library names with versions). |
| Experiment Setup | Yes | The n nodes were placed uniformly on [ n, n ]. Different dimensions d and length-scales ℓ were considered and the product Matérn kernel with smoothness parameter ρ = 5/2 (see Eqn. C15 in the supplement) was used. As in Sec. 3.2, it is apparent from Fig. 3 that the BSC is less sensitive to length-scale misspecification compared to the standard BC method. That is, we (i) assign λ the improper prior p(λ) 1/λ and marginalise over it so that the BSC posterior becomes Student-t with the mean µX(f ), variance (n 2) 1(f X) K 1 X f X σ2 X and n degrees of freedom [35, Sec. 2.2] and (ii) set ℓusing empirical Bayes (EB) based on the Gaussian log-marginal likelihood [42, Sec. 5.4.1] |