Jisu Kim, Ph.D. student seminar - Statistical Inference for Geometric Data
- Monday, May 22, 2017 from 1:00pm to 2:00pm
- Barnard Hall, 59717 - view map
In this talk, I will explore how statistical inference can be done on geometric structures. First, I will present dimension estimation problem. Many algorithms in machine learning and computational geoemtry require, as input, the intrinsic dimension of the manifold, which has to be estimated. We characterize the statistical difficulty of the dimension estimation problem by computing the minimax rate for estimating the dimension. Second, I will present reach estimation problem. Various problems in manifold estimation make use of a quantity called the reach, which is a measure of the regularity of the manifold. I will present the reach estimator and the minimax rate for estimating the reach. Third, I will present the statistical inference for cluster trees. A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. I will present methods to construct and summarize confidence sets for the unknown true cluster tree.
Jisu Kim is a Ph.D. student in Statistics and Machine Learning, Carnegie Mellon University. His research interest is mainly on statistical inference on geometrical or topological features of data. He is also the maintainer of R package TDA.