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On statistical learning of simplices: Unmixing problem revisited

Najafi, A ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1214/20-AOS2016
  3. Publisher: Institute of Mathematical Statistics , 2021
  4. Abstract:
  5. 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(Kε2 log Kε ), 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. © Institute of Mathematical Statistics, 2021
  6. Keywords:
  7. Computer simulations ; Statistical learning theory ; Sample complexity ; Inference of simplices ; High-dimensional geometry
  8. Source: Annals of Statistics ; Volume 49, Issue 3 , 2021 , Pages 1626-1655 ; 00905364 (ISSN)
  9. URL: https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-3/On-statistical-learning-of-simplices-Unmixing-problem-revisited/10.1214/20-AOS2016.short