Gaussian Processes with Linear Operator Inequality Constraints
Authors: Christian Agrell
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The numerical experiments were performed using the Python implementation available at https://github.com/cagrell/gp_constr. In Table 2 we summarize the results from running 100 of these experiments. In each experiment, Q2, PVA and AWo CI was computed from prediction at 1000 locations sampled uniformly in the domain. |
| Researcher Affiliation | Collaboration | Christian Agrell EMAIL Department of Mathematics University of Oslo P.O. Box 1053 Blindern, Oslo N-0316, Norway Group Technology and Research DNV GL P.O. Box 300, 1322 Høvik, Norway |
| Pseudocode | Yes | Algorithm 3 Sampling from the posterior distribution. Algorithm 5 Finding locations of virtual observations Xv s.t. ˆpc(x) ptarget for all x Ω. Algorithm 7 Finding locations of virtual observations Xv i s.t. ˆpc,i(x) ptarget for all x Ωand all sub-operators F1, . . . , Fk. |
| Open Source Code | Yes | A Python implementation is available at https://github.com/cagrell/gp_constr, together with the code used for the examples. |
| Open Datasets | No | The paper uses synthetic data generated from functions (e.g., f(x) = 1/3[tan−1(20x − 10) − tan−1(−10)], robot arm function, pipeline capacity equation) for its numerical examples rather than relying on pre-existing publicly available datasets. While it cites sources for the functions/models, it does not provide access information for specific datasets. |
| Dataset Splits | No | The paper describes how observations are generated (e.g., "40 observations taken from a Latin hypercube sample", "training set of N = 5nx or N = 10nx LHS samples") and how predictions are evaluated ("prediction at 1000 locations sampled uniformly"), but it does not specify explicit training/test/validation splits for a fixed dataset. The data is generated on-the-fly for each experiment. |
| Hardware Specification | Yes | We also report the probability that the constraint holds in the unconstrained GP, p(C|Y ) given in (7), and the CPU time in seconds used to generate 104 samples from the posterior on an Intel R Core TM i5-7300U 2.6GHz CPU. |
| Software Dependencies | No | The paper mentions a "Python implementation" and cites "SciPy: Open source scientific tools for Python, 2001" as being used, but it does not specify version numbers for Python or any of the libraries like SciPy. Therefore, specific software dependencies with version numbers are not provided. |
| Experiment Setup | Yes | We select an RBF kernel (16) with parameters σK = 0.5 (variance) and l = 0.1 (length scale). To represent noiseless observations we set σ2 = 10−6, where σ2 is the noise variance in the Gaussian likelihood. The assumed noise on virtual observations will also be set to 10−6. |