{"type":"ScholarlyArticle","title":"Dynamic Flows on Curved Space Generated by Labeled Data","authors":[{"name":"Xinru Hua","slug":"xinru-hua","given":"Xinru","family":"Hua","affiliation":"Stanford University , United States"},{"name":"Truyen Nguyen","slug":"truyen-nguyen","given":"Truyen","family":"Nguyen","affiliation":"The University of Akron , United States"},{"name":"Tam Le","slug":"tam-le","given":"Tam","family":"Le","affiliation":"The Institute of Statistical Mathematics / RIKEN AIP , Japan"},{"name":"Jose Blanchet","slug":"jose-blanchet","given":"Jose","family":"Blanchet","affiliation":"Stanford University , United States"},{"name":"Viet Anh Nguyen","slug":"viet-anh-nguyen","given":"Viet Anh","family":"Nguyen","affiliation":"Chinese University of Hong Kong , China"}],"abstract":"The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest (i.e., target). We lift both datasets to the space of probability distributions on the feature-Gaussian manifold, and then develop a gradient flow method that minimizes the maximum mean discrepancy loss. To perform the gradient flow of distributions on the curved feature-Gaussian space, we unravel the Riemannian structure of the space and compute explicitly the  Riemannian gradient of the loss function induced by the optimal transport metric. For practical applications, we also propose a discretized flow, and provide conditional results guaranteeing the global convergence of the flow to the optimum. We illustrate the results of our proposed gradient flow method on several real-world datasets and show our method can improve the accuracy of classification models in transfer learning settings.","doi":"10.24963/ijcai.2023/423","url":"https://ijcai.org/proceedings/2023/423","pdf":"https://ijcai.org/proceedings/2023/0423.pdf","markdown":"https://ijcai.org/proceedings/2023/423.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/423","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Machine Learning","track":"Main Track","number":423,"pages":{"first":3803,"last":3811},"keywords":["Machine Learning: ML: Optimization","Machine Learning: ML: Multi-task and transfer learning","Machine Learning: ML: Few-shot learning","Computer Vision: CV: Machine learning for vision"],"videos":[],"references":[{"position":1,"raw":"[Alvarez-Melis and Fusi, 2020] David Alvarez-Melis and Ni- colo Fusi. 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