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.