Wasserstein Proximal Coordinate Gradient Algorithms
Authors: Rentian Yao, Xiaohui Chen, Yun Yang
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical results for both motivating examples are consistent with our theoretical findings. [...] In Section 5, we demonstrate the applications of our algorithm and theory to mean-field variational inference and multi-species systems, along with numerical experiments. |
| Researcher Affiliation | Academia | Rentian Yao EMAIL Department of Statistics University of Illinois at Urbana Champaign Champaign, IL 61820, USA; Xiaohui Chen EMAIL Department of Mathematics University of Southern California Los Angeles, CA 90089, USA; Yun Yang EMAIL Department of Mathematics University of Maryland College Park, MD 20742, USA |
| Pseudocode | Yes | Algorithm 1 WPCG-P; Algorithm 2 WPCG-S; Algorithm 3 WPCG-R |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code for the described methodology, nor does it provide a link to a code repository. |
| Open Datasets | Yes | We apply the WPCG-P algorithm to analyze the Pima Indian diabetes data set (Smith et al., 1988). |
| Dataset Splits | Yes | A stratified sample of 68 data points is set aside as the test set, while the remaining 700 points constitute the training set. |
| Hardware Specification | No | The paper describes experimental setups and methods but does not provide specific details about the hardware used (e.g., GPU models, CPU types, memory). General terms like 'neural network' are used without hardware context. |
| Software Dependencies | No | The paper mentions using a 'neural network with three fully connected hidden layers' and 'activation function is Re Lu' but does not specify any software libraries (e.g., PyTorch, TensorFlow) or their version numbers. |
| Experiment Setup | Yes | In both numerical methods, B 1000 particles are used to approximate each marginal distribution. In the FA approach, a neural network with three fully connected hidden layers is used to approximate the optimal transport map. Each hidden layer consists of 1000 neurons, and the activation function is Re Lu defined as Re Lupxq maxtx, 0u. [...] In the numerical study, we consider the following test example [...] B 1000 particles are generated to approximate each species, and a neural network with 2 hidden layers is used to solve (16) in the FA approach. Each hidden layer consists of 800 neurons, and the activation function is Re Lu. |