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TITLE: [GS_M_GT] Statistical Inference on Topological Data Analysis and Application to Machine Learning.

ABSTRACT: Topological Data Analysis (TDA) generally refers to utilizing topological features from data. Typical examples are cluster tree and persistent homology. The cluster tree gathers similar data together to make clusters. The persistent homology quantifies salient topological features that appear at different resolutions of the data. TDA provides useful information, such as delivering scientific information from data, or extracting useful features for learning. The first part of this talk will be about the statistical inference on TDA. I will first present statistical inference on the cluster tree. Then, I will present how the randomness of the persistent homology computed from data can be statistically quantified and significant topological features can be identified. The second part of this talk will be about the application of TDA to machine learning. This talk will specifically focus on two aspects: featurization and evaluation. I will present how the persistent homology is featurized in Euclidean space or functional space. Then, I will end this talk by presenting how TDA can be applied to evaluate data or machine learning models.