Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks
Authors: Jiaojiao Fan, Amirhossein Taghvaei, Yongxin Chen
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In Section 4.1, we present numerical experiments on 2D/3D datasets which serve as proof of concept and qualitatively illustrate the performance of our approach. In Section 4.2, we numerically study the effects of dimensionality and demonstrate the scalability of our algorithms to high-dimensional problems. In Section 4.3 and 4.4, we apply our algorithm in tasks such as Bayesian inference with large scale dataset and color transfer. In Section 4.5, we illustrate the ability of our algorithm to serve as a generative model. |
| Researcher Affiliation | Academia | Jiaojiao Fan 1 Amirhossein Taghvaei 2 Yongxin Chen 1 1Georgia Institute of Technology 2University of California, Irvine. |
| Pseudocode | Yes | Algorithm 1 Neural Wasserstein Barycenter (NWB) Input: Marginal dist. µ1:N, Generator dist. η, Batch size M for k3 = 1, . . . , K3 do Sample batch {Zj}M j=1 η Sample batch Y i j M j=1 µi for all i = 1, , N for k2 = 1, . . . , K2 do for k1 = 1, . . . , K1 do Update all θgi to decrease (10) end for Update all θfi to increase (10) Clip: Wl = max(Wl, 0) for all θfi end for Update θh to decrease (10) end for |
| Open Source Code | Yes | Download Code at https://github.com/sbyebss/ Scalable-Wasserstein-Barycenter |
| Open Datasets | Yes | MNIST: To further investigate the performance of our algorithm in high dimension setting with real dataset, we use the MNIST data set. (...) http://archive.ics.uci.edu/ml/datasets/ Bike+Sharing+Dataset |
| Dataset Splits | No | The paper mentions splitting data into subsets for one experiment ('We randomly split the data into 5 equal-size subsets') but does not provide comprehensive train/validation/test dataset splits with percentages or specific counts needed for reproduction across all experiments. |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU/CPU models, processor types, or memory amounts used for running experiments. |
| Software Dependencies | No | The paper mentions software like 'Py MC3 library' and refers to 'Pytorch-gan' and 'pythonot.github.io', but it does not specify exact version numbers for these software dependencies (e.g., 'PyTorch 1.9'). |
| Experiment Setup | Yes | Hyper-parameter choice We choose a neural network architecture of 3 4 hidden layers of size 1 2 times of input dimension in high dim cases and size 16 32 in 2D/3D cases, with PRe LU activation function. |