Notice: 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. Full accuracy metrics and methodology are described in [1].
Wasserstein barycenters can be computed in polynomial time in fixed dimension
Authors: Jason M Altschuler, Enric Boix-Adsera
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | While the focus of this paper is theoretical, here we briefly mention that a slight variant of our algorithm can provide high-precision solutions at previously intractable problem sizes. To demonstrate this, we implement our algorithm for dimension d = 2 in Python. The only difference between our numerical implementation and the theoretical algorithm described above is that we use a standard cutting-plane method (see, e.g., (Bertsimas and Tsitsiklis, 1997, 6.3)) for the outer loop in step 1 rather than the Ellipsoid algorithm due to its good practical performance. Code and further implementation details are provided on Github.5 |
| Researcher Affiliation | Academia | Jason M. Altschuler EMAIL Enric Boix-Adser a EMAIL Laboratory for Information and Decision Systems Massachusetts Institute of Technology, Cambridge MA 02139 |
| Pseudocode | No | The paper describes the algorithm conceptually in Section 3 and its subsections, outlining the steps and theoretical foundations, but it does not include a distinct, structured block of pseudocode or a formally labeled algorithm figure. |
| Open Source Code | Yes | Code and further implementation details are provided on Github.5 |
| Open Datasets | Yes | Specifically, here we compare our barycenter algorithm against state-of-the-art methods on a standard benchmark dataset of images of nested ellipses (Cuturi and Doucet, 2014; Janati et al., 2020). |
| Dataset Splits | No | The paper describes generating 'k = 10 uniform distributions each on n = 20 points randomly drawn from [ -1,1]2 R2' and using 'k = 10 images, each of size 60 x 60' for experiments. However, it does not specify any training, validation, or test dataset splits in the conventional machine learning sense for reproducing experiments. |
| Hardware Specification | Yes | All experiments are run on a standard 2014 Lenovo Yoga 720-13IKB laptop. |
| Software Dependencies | No | The paper states, 'we implement our algorithm for dimension d = 2 in Python.' However, it does not provide specific version numbers for Python or any other libraries or frameworks used in the implementation, which are necessary for reproducible software dependencies. |
| Experiment Setup | No | The paper mentions that for comparison algorithms, 'IBP has an additional parameter: the entropic regularization γ, which significantly impacts the algorithm’s accuracy and numerical stability.' It also states that 'we binary search for the most accurate γ.' However, for the authors' own proposed algorithm, specific hyperparameters, training configurations, or system-level settings are not detailed in the main text. |