BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shing-Tung Yau (Tsinghua University\, Beijing) DTSTART:20240418T120000Z DTEND:20240418T133000Z DTSTAMP:20260423T005742Z UID:bM2L/6 DESCRIPTION:Title: Man ifold Fitting: an Invitation to Machine Learning – a Mathematician’s v iew\nby Shing-Tung Yau (Tsinghua University\, Beijing) as part of Barc elona Mathematics and Machine Learning Colloquium Series\n\n\nAbstract\nNa tural datasets have intrinsic patterns\, which can be summarized as the ma nifold distribution principle: the distribution of a class of data is clos e to a low-dimensional manifold. The manifold fitting problem can go back to the solution to the Whitney extension problem leading to new insights f or data interpolation. Assume that we are given a set $Y\\subseteq\\mathbb {R}^D$. When can we construct a smooth d-dimensional submanifold $\\wideha t{M}\\subseteq\\mathbb{R}^D$ to approximate $Y$\, and how well can $\\wide hat{M}$ estimate $Y$ in terms of distance and smoothness? However\, many o f these methods rely on restrictive assumptions\, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational elem ent in data science\, the manifold fitting problem\, merits further explor ation and discussion within the modern data science community. The talk wi ll be partially based on some recent works [4\, 2\, 3\, 1] along with some on-going progress.\n\n[1] Zhigang Yao\, Bingjie Li\, Yukun Lu\, and Shing -Tung Yau. Single-cell analysis via manifold fitting: A new framework for RNA clustering and beyond\, 2024.\n\n[2] Zhigang Yao\, Jiaji Su\, Bingjie Li\, and Shing-Tung Yau. Manifold fitting. arXiv preprint 2304.07680\, 202 3.\n\n[3] Zhigang Yao\, Jiaji Su\, and Shing-Tung Yau. Manifold fitting wi th cycleGAN. Proceedings of the National Academy of Sciences of the United States of America\, 121(5):e2311436121\, 2023.\n\n[4] Zhigang Yao and Yuq ing Xia. Manifold fitting under unbounded noise. arXiv preprint 1909.10228 \, 2019.\n LOCATION:https://researchseminars.org/talk/bM2L/6/ END:VEVENT END:VCALENDAR