- Journal Article
We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of `spectral unmixing'. We theoretically show that a sufficient sample complexity for reliable learning of a K-dimensional simplex up to a total-variation error of ϵ is O(K2/ϵ log K/ϵ), which yields a substantial improvement over existing bounds. Based on our new theoretical framework, we also propose a heuristic approach for the inference of simplices. Experimental results on synthetic and real-world datasets demonstrate a comparable performance for our method on noiseless samples, while we outperform the state-of-the-art in noisy cases. Show more
Journal / seriesThe Annals of Statistics
Pages / Article No.
PublisherInstitute of Mathematical Statistics
Subjectcomputer simulations; high-dimensional geometry; Inference of simplices; sample complexity; statistical learning theory
Organisational unit03457 - Welzl, Emo / Welzl, Emo
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