Schedule

MINDS SEMINAR

MINDS Seminar Series | Jisu Kim (Seoul National University) - Statistical Inference For Geometric and Topological Data

MINDS SEMINAR
period : 2024-03-26 ~ 2024-03-26
time : 17:00:00 ~ 18:00
개최 장소 : Math Bldg 404 & Online streaming (Zoom)
Topic : Statistical Inference For Geometric and Topological Data
개요
Date 2024-03-26 ~ 2024-03-26 Time 17:00:00 ~ 18:00
Speaker Jisu Kim Affiliation Seoul National University
Place Math Bldg 404 & Online streaming (Zoom) Streaming link ID : 688 896 1076 / PW : 54321
Topic Statistical Inference For Geometric and Topological Data
Contents Geometric and topological structures can aid statistics in several ways. In high dimensional statistics, geometric structures can be used to reduce dimensionality. High dimensional data entails the curse of dimensionality, which can be avoided if there are low dimensional geometric structures. On the other hand, geometric and topological structures also provide useful information. Structures may carry scientific meaning about the data and can be used as features to enhance supervised or unsupervised learning. In this talk, I will explore how statistical inference can be done on geometric and topological structures. First, given a manifold assumption, I will explore the minimax rate for estimating the dimension of the manifold. Second, also under the manifold assumption, I will explore the minimax rate for estimating the reach, which is a regularity quantity depicting how a manifold is smooth and far from self-intersecting. Third, I will investigate inference on cluster trees, which is a hierarchy tree of high-density clusters of a density function. Fourth, I will investigate inference on persistent homology, which quantifies salient topological features that appear at different resolutions of the data.
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