Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Consistency of Gaussian Process Regression in Metric Spaces
Authors: Peter Koepernik, Florian Pfaff
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we examine formal consistency of GP regression on general metric spaces. Specifically, we consider a GP prior on an unknown real-valued function with a metric domain space and examine consistency of the resulting posterior distribution. If the kernel is continuous and the sequence of sampling points lies sufficiently dense, then the variance of the posterior GP is shown to converge to zero almost surely monotonically and in Lp for all p > 1, uniformly on compact sets. Moreover, we prove that if the difference between the observed function and the mean function of the prior lies in the reproducing kernel Hilbert space of the prior s kernel, then the posterior mean converges pointwise in L2 to the unknown function, and, under an additional assumption on the kernel, uniformly on compacts in L1. This paper provides an important step towards the theoretical legitimization of GP regression on manifolds and other non-Euclidean metric spaces. Keywords: Gaussian process, regression, nonparametric inference, Bayesian inference, reproducing kernel Hilbert space |
| Researcher Affiliation | Academia | Peter Koepernik EMAIL Department of Statistics University of Oxford 24 29 St Giles , Oxford OX1 3LB, United Kingdom Florian Pfaff EMAIL Intelligent Sensor-Actuator-Systems Laboratory Karlsruhe Institute of Technology Adenauerring 2, 76131 Karlsruhe, Germany |
| Pseudocode | No | The paper primarily consists of mathematical definitions, theorems, lemmas, and proofs. It does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to any code repositories or mention code in supplementary materials. |
| Open Datasets | No | The paper is a theoretical work focusing on consistency proofs for Gaussian process regression in metric spaces. It does not involve experimental evaluation or the use of any specific datasets. |
| Dataset Splits | No | The paper is a theoretical work and does not use any datasets. Therefore, there is no mention of dataset splits. |
| Hardware Specification | No | The paper is theoretical, focusing on mathematical proofs and consistency. It does not describe any experiments that would require specific hardware, and thus no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical, focusing on mathematical proofs and consistency. It does not describe any implemented experiments or software, and thus no software dependencies or version numbers are mentioned. |
| Experiment Setup | No | The paper is a theoretical work providing mathematical proofs for the consistency of Gaussian process regression. It does not describe any experimental setups, hyperparameters, or training configurations. |