Exploring the Curse of Dimensionality - Part II. - Dr. Juan Camilo Orduz

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I continue exploring the curse of dimensionality. Following the analysis form Part I., I want to discuss another consequence of sparse sampling in high dimensions: sample points are close to an edge of the sample. This post is based on The Elements of Statistical Learning, Section 2.5, which I encourage to read! Consider \(N\) data points uniformly distributed in a \(p\)-dimensional unit ball centered at the origin. Suppose we consider a nearest-neighbor estimate at the origin.