AF: EAGER: Collaborative Research: Integration of Computational Geometry and Statistical Learning for Modern Data Analysis

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Data analysis is a fundamental problem in computational science, ubiquitous in a broad range of application fields, from computer graphics to geographics information system, from sensor networks to social networks, and from economics to biological science. Two complementary fields that have driven modern data analysis are computational geometry and statistical learning. The former focuses on detailed and precise models characterizing low-dimensional geometric phenomena. The latter focuses on robust or predictive inference of models given noisy high-dimensional data. This project aims to initiate a dialog between these two fields with geometry being the central theme. A closer interaction between them will benefit and advance both fields, and can potentially fundamentally change the way we view and perform data analysis. Specifically, on one hand, the type of data common in the learning community poses several challenges for traditional computational geometry methods. The shift of focus to these challenges and the modeling of uncertainty central in statistical learning can broaden the scope of computational geometry, and lead to geometric algorithms and models that are more robust to noise and extend to high-dimensional data analysis. On the other hand, computational geometry has developed many elegant structures that contain often detailed and precise information about the underlying domain. Models parameterized using these structures can lead to statistical learning models and algorithms that are richer and more interpretable but remain robust to noise and are predictive. This project is multi-disciplinary in nature, and will involve fields including computational geometry, algorithms, statistics, differential geometry and topology. Education will be integrated in this project.