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.