Inference for Gaussian Processes with Matern Covariogram on Compact Riemannian Manifolds
Authors: Didong Li, Wenpin Tang, Sudipto Banerjee
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The circle is studied as a specific example of compact Riemannian manifolds with numerical experiments to illustrate and corroborate the theory. Figure 1(b) shows a set of simulated Z s with different values of α. Figure 2 shows that bσ2 1,n σ2 1 := σ2 0α0 sinh(α0/2) C ν,α1 α1 sinh(α1/2) as shown by the horizontal line and the empirical distribution of n bσ2 1,n σ2 1 1 is N(0, 2), for ν = 1/2, σ0 = 0.1, α0 = 2 = α1 = 1. Panel (a) supports Theorem 9 empirically. That is, although (σ2, α, ν) are not consistently estimable, the microergodic parameter σ2α sinh(α/2) C ν,α is consistently estimable. Panel (b) supports our conjecture after Theorem 6 empirically. |
| Researcher Affiliation | Academia | Didong Li EMAIL Department of Biostatistics University of North Carolina at Chapel Hill Chapel Hill, NC 27599, USA Wenpin Tang EMAIL Department of Industrial Engineering and Operations Research, Columbia University New York, NY 10027, USA Sudipto Banerjee EMAIL Department of Biostatistics University of California, Los Angeles Los Angeles, CA 90095 USA |
| Pseudocode | No | The paper focuses on theoretical derivations, proofs, and numerical illustrations of concepts. It does not contain any sections or figures explicitly labeled as 'Pseudocode' or 'Algorithm', nor does it present any structured, step-by-step procedures in a code-like format. |
| Open Source Code | No | The paper states: 'c 2023 Didong Li, Wenpin Tang and Sudipto Banerjee. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v24/22-0503.html.' This refers to the licensing of the paper itself, not the release of source code for the methodology described in the paper. There is no explicit statement about code availability or a link to a code repository. |
| Open Datasets | No | Figure 1(b) shows a set of simulated Z s with different values of α. Figure 3(b) shows some simulated Z s with different α s. The paper describes numerical experiments using simulated data generated by the authors, rather than referencing or providing access to any pre-existing publicly available or open datasets. |
| Dataset Splits | No | The paper uses simulated data for numerical illustrations, as shown in figures like 1(b), 2, and 3(b). Since the data is simulated to demonstrate theoretical concepts, there are no traditional training, validation, or test dataset splits typically associated with empirical machine learning experiments. The text does not mention any specific splitting methodologies or percentages. |
| Hardware Specification | No | The paper describes 'numerical experiments to illustrate and corroborate the theory' and 'numerical simulation experiment'. However, it does not provide any specific details regarding the hardware (e.g., GPU models, CPU types, memory specifications, or cloud computing platforms) used to conduct these experiments. |
| Software Dependencies | No | The paper discusses theoretical concepts and numerical simulations without specifying the software or libraries used for these simulations. There are no mentions of programming languages, statistical packages, or specific software versions (e.g., Python, R, PyTorch, TensorFlow with version numbers). |
| Experiment Setup | Yes | Figure 2 shows that bσ2 1,n σ2 1 := σ2 0α0 sinh(α0/2) C ν,α1 α1 sinh(α1/2) as shown by the horizontal line and the empirical distribution of n bσ2 1,n σ2 1 1 is N(0, 2), for ν = 1/2, σ0 = 0.1, α0 = 2 = α1 = 1. Figure 1(b) and Figure 3(b) depict 'Sample fields with σ2 = 0.1, ν = 1/2, α {0.01, 1, 100}'. These are specific parameter values used in the numerical simulations. |