On statistical learning of simplices: Unmixing problem revisited
Amir Najafi, Saeed Ilchi, Amir Hossein Saberi, Seyed Abolfazl Motahari, Babak H. Khalaj, Hamid R. Rabiee
The Annals of Statistics · 2021 · Volume 49 · Issue 3
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 O(K2ϵlogKϵ), 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.
Keywords
62F99, computer simulations, high-dimensional geometry, Inference of simplices, sample complexity, statistical learning theory
Enable JavaScript for citation tools and additional paper interactions.