Linear cost and exponentially convergent approximation of Gaussian Matérn processes on intervals
Authors: David Bolin, Vaibhav Mehandiratta, Alexandre B. Simas
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Besides theoretical justifications, we demonstrate accuracy empirically through carefully designed simulation studies, which show that the method outperforms state-of-the-art alternatives in accuracy for fixed computational cost in tasks like Gaussian process regression. |
| Researcher Affiliation | Academia | David Bolin EMAIL CEMSE Division, statistics program King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia Vaibhav Mehandiratta EMAIL CEMSE Division, statistics program King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia Alexandre B. Simas EMAIL CEMSE Division, statistics program King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia |
| Pseudocode | No | The paper describes methods and propositions but does not present any structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | The proposed method is implemented in the R package r SPDE (Bolin and Simas, 2023) available on CRAN, and all code for the comparisons, as well as a Shiny application with further results can be found in https://github.com/vpnsctl/Markov Approx Matern/. |
| Open Datasets | No | We first consider the case of a dataset with 5000 observations, y = [y1, y2, . . . , yn], with the observation locations being evenly spaced over the interval I = [0, 50]. Each observation is generated as yi | u( ) N(u(ti), σ2 e), where ti are the observation locations, and u is a centered Gaussian process with the Matérn covariance function given by (1). This indicates that the data was synthetically generated for the study, not obtained from an existing public dataset. |
| Dataset Splits | Yes | We first consider the case of a dataset with 5000 observations, y = [y1, y2, . . . , yn], with the observation locations being evenly spaced over the interval I = [0, 50]. ... The goal is to compute the posterior mean µu|y with elements (µu|y)j = E(u(pj)|y), and the posterior standard deviation σu|y with elements (σu|y)j = pVar(u(pj)|y), where pj are the prediction locations. To make the comparison simple, we initially choose pj = tj evenly spaced in the interval. ... In Scenario 1, we consider a forecasting setting where we construct a regular mesh of 1501 points in the interval [0, 15]. The first 1001 points, evenly spaced in [0, 10], serve as observation locations. For prediction, we use all observation locations plus the next n {0, 1, . . . , 10, 20, 30, 40, 50, 75, 100, 125, . . . , 500} consecutive points from the mesh as prediction locations. In Scenario 2, we instead use 250 observation locations randomly sampled uniformly in the interval [0, 10], with a minimum spacing of 10 3 between locations ensured through resampling if needed, to ensure stability for nn GP. For an increasing sequence of values n between 0 and 3000, we consider n evenly spaced prediction locations in the interval. |
| Hardware Specification | Yes | The results were obtained using a Mac Book Pro Laptop with an M3 Max processor and 128Gb of memory, without using any parallel computations to make the comparison as fair as possible. |
| Software Dependencies | Yes | The proposed method is implemented in the R package r SPDE (Bolin and Simas, 2023) available on CRAN, and all code for the comparisons, as well as a Shiny application with further results can be found in https://github.com/vpnsctl/Markov Approx Matern/. The paper also mentions 'R-INLA (Lindgren and Rue, 2015)' and 'inlabru (Bachl et al., 2019)'. |
| Experiment Setup | Yes | We set σ = 1 (as it is merely a scaling parameter) and explore two different noise levels: σe = 0.1 and 0.1. Additionally, we vary the smoothness parameter ν over the interval (0, 2.5). For each value of ν, we choose κ = 2ν, ensuring that the practical correlation range, ρ = 8ν/κ, remains fixed at 2. ... The total prediction times were averaged over 100 samples to obtain the calibrations. |