Bayesian Quadrature on Riemannian Data Manifolds
Authors: Christian Fröhlich, Alexandra Gessner, Philipp Hennig, Bernhard Schölkopf, Georgios Arvanitidis
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate accuracy and performance of our approach on synthetic and real-world data manifolds, where we observe speedups by factors of up to 20. In these examples we focus on the LAND model, which provides a wide range of numerical integration problems of varying geometry and difficulty. We highlight molecular dynamics as a promising application area for Riemannian machine learning models. The results support the use of probabilistic numerical methods within Riemannian geometry to achieve significant speedup. |
| Researcher Affiliation | Academia | 1University of T ubingen, Germany 2Max Planck Institute for Intelligent Systems, T ubingen, Germany. |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | Yes | Code is publicly available at github.com/froec/BQon RDM. |
| Open Datasets | Yes | We trained a Variational Auto-Encoder on the first three digits of MNIST... We obtained multiple trajectories of the closed to open transition of the enzyme adenylate kinase (ADK) (Seyler et al., 2015). |
| Dataset Splits | No | The paper mentions using well-known datasets like MNIST but does not explicitly provide specific training/validation/test splits (e.g., percentages, sample counts, or explicit standard split citations) needed for reproduction in the main text. |
| Hardware Specification | No | The paper does not explicitly describe any specific hardware components (e.g., GPU/CPU models, memory) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific version numbers for software dependencies used in the experiments. |
| Experiment Setup | Yes | We fix the number of acquired samples for BQ and generate boxplots from the mean errors on the whole LAND fit for 16 independent runs... We let WSABI-L and WSABI-M actively collect 80 in the former and 10 samples additionally to the reused ones in the latter case; for DCV, we fix 18 and 2 exponential maps, respectively, and acquire 6 points on each straight line. |