Notice: This website is continuously updated as new conference proceedings and journal volumes are published. Consequently, the figures presented here may differ from those reported in our publications.
A brief overview of our methodology is provided on the Methods page, along with references to publications documenting our approach and links to the code and data used in each study.
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.
Stochastic Wasserstein Barycenters
Authors: Sebastian Claici, Edward Chien, Justin Solomon
ICML 2018 | Venue PDF | LLM Run Details | Input Tokens: 16,417 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 4,306 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 7. Experiments We showcase the versatility of our method on several applications. We typically use between 16K and 256K samples per input distribution to approximate the power cell density and barycenter. |
| Researcher Affiliation | Academia | 1Computer Science and Artifical Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, USA. Correspondence to: Sebastian Claici <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Optimizing estimate of barycenter support Require: Estimate of barycenter support Σ = {xi}m i=1 Ensure: Optimized barycenter support Σ with lower cost. |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that the source code for the described methodology is publicly available. |
| Open Datasets | No | The paper uses synthetic or generated distributions (e.g., 'mixture of ten Gaussians', 'uniform distributions over lines', 'randomly generated ellipses', 'uniform distributions on the unit square', 'discrete distribution over the image pixels proportional to intensity') without providing specific access information (links, DOIs, repositories, or formal citations to established public datasets). |
| Dataset Splits | No | The paper does not provide specific details on dataset splits (e.g., percentages or sample counts for training, validation, or testing). |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory, or specific cloud instances) used for conducting the experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers (e.g., Python, PyTorch, CUDA versions, or specific solver versions). |
| Experiment Setup | Yes | In our experiments, we use α = 10^-3 and β = 0.99. Convergence of the accelerated gradient method can be shown when α = 1/L where L is the Lipschitz constant of F; in 6, we give an estimate of this constant. Our convergence criterion for this step is ||F||_2^2 < ε. We typically use between 16K and 256K samples per input distribution to approximate the power cell density and barycenter. The variance is due to different problem sizes and dimensionality of the input measures. We stop the gradient ascent step when ||F||_2^2 < 10^-6. |