Riemannian Continuous Normalizing Flows

Authors: Emile Mathieu, Maximilian Nickel

NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We empirically demonstrate the advantages of our method on constant curvature manifolds i.e., the Poincaré disk and the sphere and show the benefits of the proposed approach compared to non Riemannian and projected methods for maximum likelihood estimation and reverse KL minimization. We also apply our method to density estimation on earth-sciences data (e.g., locations of earthquakes, floods and wildfires) and show that it yields better generalization performance and faster convergence.
Researcher Affiliation Collaboration Emile Mathieu , Maximilian Nickel emile.mathieu@stats.ox.ac.uk, maxn@fb.com Department of Statistics, University of Oxford, UK Facebook Artificial Intelligence Research, New York, USA
Pseudocode No The paper does not contain any clearly labeled pseudocode or algorithm blocks.
Open Source Code No The paper does not provide an explicit statement or link for open-source code.
Open Datasets Yes To this extent, we gathered four earth location datasets, representing respectively volcano eruptions (NOAA, 2020b), earthquakes (NOAA, 2020a), floods (Brakenridge, 2017) and wild fires (EOSDIS, 2020).
Dataset Splits No The paper mentions splitting datasets into
Hardware Specification No The paper does not specify any hardware details like GPU models, CPU types, or cloud instances used for experiments.
Software Dependencies No The paper mentions
Experiment Setup Yes For all projected models (e.g. stereographic and wrapped cf Section 3), the vector field s architecture is chosen to be a multilayer perceptron as in Grathwohl et al. (2019), whilst the architecture described in Section 2 is used for our Riemannian (continuous normalizing flow) model. For fair comparisons, we also parametrize projected models with a CNF. Also, all models are chosen to have approximately the same number of parameters. All models were implemented in Py Torch (Paszke et al., 2017) and trained by stochastic optimization with Adam (Kingma and Ba, 2015). All 95% confidence intervals are computed over 12 runs. Please refer to Appendix G for full experimental details.