{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sliced-wasserstein-distance-for-learning","title":"Sliced Wasserstein Distance for Learning Gaussian Mixture Models","arxiv_id":"1711.05376","date":"2017-11-15","proceeding":"CVPR 2018 6","authors":["Soheil Kolouri","Gustavo K. Rohde","Heiko Hoffmann"],"abstract":"Gaussian mixture models (GMM) are powerful parametric tools with many\napplications in machine learning and computer vision. Expectation maximization\n(EM) is the most popular algorithm for estimating the GMM parameters. However,\nEM guarantees only convergence to a stationary point of the log-likelihood\nfunction, which could be arbitrarily worse than the optimal solution. Inspired\nby the relationship between the negative log-likelihood function and the\nKullback-Leibler (KL) divergence, we propose an alternative formulation for\nestimating the GMM parameters using the sliced Wasserstein distance, which\ngives rise to a new algorithm. Specifically, we propose minimizing the\nsliced-Wasserstein distance between the mixture model and the data distribution\nwith respect to the GMM parameters. In contrast to the KL-divergence, the\nenergy landscape for the sliced-Wasserstein distance is more well-behaved and\ntherefore more suitable for a stochastic gradient descent scheme to obtain the\noptimal GMM parameters. We show that our formulation results in parameter\nestimates that are more robust to random initializations and demonstrate that\nit can estimate high-dimensional data distributions more faithfully than the EM\nalgorithm.","url_abs":"http://arxiv.org/abs/1711.05376v2","url_pdf":"http://arxiv.org/pdf/1711.05376v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"sliced-wasserstein-distance-for-learning","repo_url":"https://github.com/skolouri/swgmm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"sliced-wasserstein-distance-for-learning","repo_url":"https://github.com/yokaze/swgmm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1711.05376","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}