Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization

Authors: Alexander Korotin, Lingxiao Li, Justin Solomon, Evgeny Burnaev

ICLR 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We provide theoretical analysis on error bounds as well as empirical evidence of the effectiveness of the proposed approach in low-dimensional qualitative scenarios and high-dimensional quantitative experiments.
Researcher Affiliation Academia Alexander Korotin Skolkovo Institute of Science and Technology Advanced Data Analytics in Science and Engineering Group Moscow, Russia a.korotin@skoltech.ru Lingxiao Li Massachusetts Institute of Technology Geometric Data Processing Group Cambridge, Massachusetts, USA lingxiao@mit.edu Justin Solomon Massachusetts Institute of Technology Geometric Data Processing Group Cambridge, Massachusetts, USA jsolomon@mit.edu Evgeny Burnaev Skolkovo Institute of Science and Technology Advanced Data Analytics in Science and Engineering Group Moscow, Russia e.burnaev@skoltech.ru
Pseudocode Yes Algorithm 1: Numerical Procedure for Optimizing Multiple Correlations (14)
Open Source Code Yes The code is written on Py Torch framework and is publicly available at https://github.com/iamalexkorotin/Wasserstein2Barycenters.
Open Datasets Yes Analogous to (Li et al., 2020), we consider Poisson and negative binomial regressions for predicting the hourly number of bike rentals using features such as the day of the week and weather conditions.2
Dataset Splits No The paper describes splitting the data into N=5 equally-sized subsets for subset posterior aggregation in Section 5.2: 'We randomly split the data into N = 5 equally-sized subsets and obtain 105 samples from each subset posterior using the Stan library (Carpenter et al., 2017).' However, it does not specify explicit training, validation, and test dataset splits in the conventional sense (e.g., percentages or counts for model training and evaluation).
Hardware Specification Yes The networks are trained on a single GTX 1080Ti.
Software Dependencies No The code is written using the Py Torch framework. We use Adam optimizer by (Kingma & Ba, 2014). While PyTorch and Adam are mentioned, no specific version numbers are provided for these software dependencies.
Experiment Setup Yes We set batch size K = 1024 and balancing coefficient γ = 0.2. We use Adam optimizer by (Kingma & Ba, 2014) with a fixed learning rate 10 3. The total number of iterations is set to 50000.