Scalable Sobolev IPM for Probability Measures on a Graph
Authors: Tam Le, Truyen Nguyen, Hideitsu Hino, Kenji Fukumizu
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 6. Experiments In this section, we illustrate the fast computation for the regularized Sobolev IPM, which is comparable to the Sobolev transport (ST), and several-order faster than the standard optimal transport (OT) for measures on a graph. We then show preliminary evidences on the advantages of the regularized Sobolev IPM kernels to compare probability measures on a given graph under the same settings for document classification and for TDA. |
| Researcher Affiliation | Academia | 1Department of Advanced Data Science, The Institute of Statistical Mathematics (ISM), Tokyo, Japan 2The University of Akron, Ohio, US. Correspondence to: Tam Le <EMAIL>. |
| Pseudocode | No | The paper only describes methods in paragraph text and mathematical formulations. There are no clearly labeled pseudocode or algorithm blocks in the main text or appendices. |
| Open Source Code | Yes | Additionally, we have released code for our proposed approach.1 1The code repository is on https://github.com/ lttam/Sobolev-IPM. |
| Open Datasets | Yes | We consider 4 popular document datasets: TWITTER, RECIPE, CLASSIC, AMAZON... We consider orbit recognition on the synthesized Orbit dataset (Adams et al., 2017), and object classification on a 10-class subset of MPEG7 dataset (Latecki et al., 2000) as in Le et al. (2022). |
| Dataset Splits | Yes | We randomly split each dataset into 70%/30% for training and test respectively, with 10 repeats, and use 1-vs-1 strategy for SVM classification. |
| Hardware Specification | No | For computational devices, we run all of our experiments on commodity hardware. |
| Software Dependencies | No | The paper mentions using 'word2vec word embedding' and 'kernelized support vector machine (SVM)' but does not provide specific version numbers for any software dependencies or libraries. |
| Experiment Setup | Yes | Typically, hyper-parameters are chosen via cross validation. Concretely, SVM regularization is chosen from {0.01, 0.1, 1, 10}, and kernel hyperparameter is chosen from {1/qs, 1/(2qs), 1/(5qs)} with s = 10, 20, . . . , 90, where we write qs for the s% quantile of a subset of corresponding distances on training set. |