Interior-Point Methods Strike Back: Solving the Wasserstein Barycenter Problem
Authors: DongDong Ge, Haoyue Wang, Zikai Xiong, Yinyu Ye
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | A numerical comparison on various distributions with existing algorithms exhibits the computational advantages of our approach. Moreover, we demonstrate the practicality of our algorithm on image benchmark problems including MNIST and Fashion-MNIST. |
| Researcher Affiliation | Academia | Dongdong Ge Research Institute for Interdisciplinary Sciences Shanghai University of Finance and Economics ge.dongdong@mail.shufe.edu.cn; Haoyue Wang School of Mathematical Sciences Fudan University haoyuewang14@fudan.edu.cn; Zikai Xiong School of Mathematical Sciences Fudan University zkxiong16@fudan.edu.cn; Yinyu Ye Department of Management Science and Engineering Stanford University yyye@stanford.edu |
| Pseudocode | Yes | Algorithm 1: Solver for the normal equation ( AD AT )z = f; Algorithm 2: SLRM for the system (A1 + A2)x = g |
| Open Source Code | No | The paper refers to 'The Matlab codes4 by J.Ye et al. [54] and set the maximum iterate number respectively 4000 and 105. 4Available in https://github.com/bobye/WBC_Matlab'. This link is for code by another research group, not the authors' own implementation described in the paper. |
| Open Datasets | Yes | Moreover, we demonstrate the practicality of our algorithm on image benchmark problems including MNIST and Fashion-MNIST. |
| Dataset Splits | No | The paper describes how image data is selected (e.g., 'randomly select 200 images for digit 8', 'resize each image to 0.5, 1, 2 times'), but it does not specify explicit training, validation, and test splits (e.g., percentages or counts for each set). |
| Hardware Specification | Yes | All experiments are run in Matlab R2018b on a workstation with two processors, Intel(R) Xeon(R) Processor E5-2630@2.40Ghz (8 cores and 16 threads per processor) and 64GB of RAM, equipped with 64-bit Windows 10 OS. |
| Software Dependencies | Yes | All experiments are run in Matlab R2018b |
| Experiment Setup | Yes | For MAAIPM, we terminate it when (b λk c xk)/(1 + |b λk| + |c xk|) is less than 5 10 5. For BADMM, we follow the algorithm 4 in [54] to implement and terminate when Π(k,1) Π(k,2) F /(1 + Π(k,1) F + Π(k,2) F ) < 10 5. For IBP, we follow the remark 3 in [9] to implement the method, terminate it when {u(n) k } {u(n 1) k } F /(1 + {u(n) k } F + {u(n 1) k } F ) < 10 8 and {v(n) k } {v(n 1) k } F /(1 + {v(n) k } F + {v(n 1) k } F ) < 10 8, and choose the regularization parameter ϵ from {0.1, 0.01, 0.001} in our experiments. For BADMM and IBP, we implement the Matlab codes4 by J.Ye et al. [54] and set the maximum iterate number respectively 4000 and 105. |