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].
Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees
Authors: Alexander Terenin, David R. Burt, Artem Artemev, Seth Flaxman, Mark van der Wilk, Carl Edward Rasmussen, Hong Ge
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We investigate the performance of the clustered-data inducing point approximation on a series of tests designed to illustrate both the behavior of its components and the overall picture. Each experiment focuses on a different aspect of the method, including approximation error, scalability, and behavior under varying quantities of data and inducing points. Full details regarding the experimental setup are given in Appendix D. ... Results can be seen in Figure 4. ... Results can be seen in Figure 5. |
| Researcher Affiliation | Collaboration | Alexander Terenin University of Cambridge and Imperial College London; David R. Burt University of Cambridge and MIT; Artem Artemev Imperial College London and Secondmind; Seth Flaxman University of Oxford; Mark van der Wilk Imperial College London and University of Oxford; Carl Edward Rasmussen University of Cambridge and Secondmind; Hong Ge University of Cambridge |
| Pseudocode | Yes | Algorithm 12 Cover Tree Inducing Points: 1: input spatial resolution ε > 0 and dataset x. Define notation Bz(R) = {x X : z x R}. 2: Initialize root node z0,1 = 1 N PN i=1 xi, assigned data A1,1 = x, R-neighbors R1,1 = {1}, as well as constants dmax = maxi=1,..,N z1,1 xi , L = log2 dmax ε , M0 = 1, and R0 = 2Lε. ... |
| Open Source Code | Yes | Equal contribution. Code available at: https://github.com/awav/conjugate-gradient-sparse-gp. |
| Open Datasets | Yes | We evaluated the different methods on two datasets: the two-dimensional East Africa geospatial dataset studied by Wan et al. (2002), Weiss et al. (2014), and Ton et al. (2018), and the four-dimensional Combined Cycle Power Plant dataset from the UCI Machine Learning Repository (Tüfekci, 2014; Dua and Graff, 2017). |
| Dataset Splits | Yes | For the two-dimensional East Africa land surface temperature dataset, we split the dataset into training and testing sets of size 55884 and 27525, respectively. |
| Hardware Specification | Yes | All experiments were run on a single Nvidia V100 GPU with 32GB RAM in double precision, except for Figure 6 where floating-point precision was used instead. |
| Software Dependencies | No | We ran experiments with using the sparse Gaussian process regression (SGPR) implementation from GPflow (Matthews et al., 2017) and a GPflow-based implementation of the clustered-data Gaussian process using stochastic maximum marginal likelihood training described in Appendix B.2. The paper mentions software by name (GPflow) but does not provide specific version numbers. |
| Experiment Setup | Yes | Both Gaussian process models were initialized with 0.1 likelihood noise and configured with a squared exponential kernel with automatic relevance determination. The length scales of the kernel were initialized to 1.0. The inducing points were set using a cover tree with the spatial resolution 0.03 0.09. ... For both models hyperparameters were trained using mini-batch stochastic optimization via the Adam optimizer, with constant learning rate 0.01 and batch size 1000. |