Abstract
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 , 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.
Citation
Amir Najafi. Saeed Ilchi. Amir Hossein Saberi. Seyed Abolfazl Motahari. Babak H. Khalaj. Hamid R. Rabiee. "On statistical learning of simplices: Unmixing problem revisited." Ann. Statist. 49 (3) 1626 - 1655, June 2021. https://doi.org/10.1214/20-AOS2016
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