Contraction rates for sparse variational approximations in Gaussian process regression
Authors: Dennis Nieman, Botond Szabo, Harry van Zanten
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We study the theoretical properties of a variational Bayes method in the Gaussian Process regression model. ... The theoretical findings are demonstrated by numerical experiments. ... Finally we conclude our results with a brief numerical study in Section 7. ... 7. Numerical experiments We illustrate the theoretical results by two numerical experiments, varying both the kernel and the choice of inducing variables. |
| Researcher Affiliation | Academia | Dennis Nieman EMAIL Department of Mathematics Vrije Universiteit Amsterdam De Boelelaan 1111, 1081 HV Amsterdam The Netherlands; Botond Szabo EMAIL Department of Decision Sciences, Bocconi Institute for Data Science and Analytics, Bocconi University Via Roentgen 1, Milano, Italy; Harry van Zanten EMAIL Department of Mathematics Vrije Universiteit Amsterdam De Boelelaan 1111, 1081 HV Amsterdam The Netherlands |
| Pseudocode | No | No structured pseudocode or algorithm blocks are explicitly present in the paper. The methodology is described using mathematical formulations. |
| Open Source Code | No | The paper does not contain any explicit statements about providing open-source code, nor does it include links to code repositories. |
| Open Datasets | No | 7.1 Matérn kernel method 1 We simulate n = 3000 samples xi uniform[0, 1] and yi N(f0(xi), σ2) with σ = 0.2 and f0(x) = |x 0.4|α |x 0.2|α for α = 0.6 ... 7.2 Squared exponential kernel method 2 In a similar fashion, we simulate n = 5000 samples xi N(0, 1) and yi from the N(f0(xi), σ2) distribution with f0(x) = |x + 1|α |x + 3/2|α for α = 0.8 and σ = 0.2. The datasets are simulated for the numerical experiments, not taken from publicly available sources. |
| Dataset Splits | No | The numerical experiments use simulated data, but the context is not about model evaluation on typical train/test/validation splits. It involves simulating data to analyze posterior contraction rates. Therefore, specific dataset splits for reproduction are not applicable or mentioned. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for the numerical experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers. |
| Experiment Setup | Yes | 7. Numerical experiments We illustrate the theoretical results by two numerical experiments, varying both the kernel and the choice of inducing variables. 7.1 Matérn kernel method 1 We simulate n = 3000 samples xi uniform[0, 1] and yi N(f0(xi), σ2) with σ = 0.2 and f0(x) = |x 0.4|α |x 0.2|α for α = 0.6 ... We use the Matérn-α kernel for the GP prior and study the variational posterior using the inducing variables obtained from the covariance matrix (Section 5.1). ... 7.2 Squared exponential kernel method 2 In a similar fashion, we simulate n = 5000 samples xi N(0, 1) and yi from the N(f0(xi), σ2) distribution with f0(x) = |x + 1|α |x + 3/2|α for α = 0.8 and σ = 0.2. ... We use the squared exponential kernel as defined in (32) with b = bn = 4n 1/(1+2α) and the variational Bayes method with operator eigenvectors (Section 5.2) as the inducing variables. |