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Geometric Inference for Probability Distribution

Geometric Inference for Probability Distribution

This video was recorded at Machine Learning Summer School (MLSS), Chicago 2009. Data often comes in the form of a point cloud sampled from an unknown compact subset of Euclidean space. The general goal of geometric inference is then to recover geometric and topological features (Betti numbers, curvatures,...) of this subset from the approximating point cloud data. In recent years, it appeared that the study of distance functions allows to address many of these questions successfully. However, one of the main limitations of this framework is that it does not cope well with outliers nor with background noise. In this talk, we will show how to extend the framework of distance functions to overcome this problem. Replacing compact subsets by measures, we will introduce a notion of distance... Show More
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