On learning sparsely used dictionaries from incomplete samples

Thanh V. Nguyen, Akshay Soni, Chinmay Hegde

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Existing algorithms for dictionary learning assume that the entries of the (high-dimensional) input data are fully observed. However, in several practical applications, only an incomplete fraction of the data entries may be available. For incomplete settings, no provably correct and polynomialtime algorithm has been reported in the dictionary learning literature. In this paper, we provide provable approaches for learning - from incomplete samples - a family of dictionaries whose atoms have sufficiently "spread-out" mass. First, we propose a descent-style iterative algorithm that linearly converges to the true dictionary when provided a sufficiently coarse initial estimate. Second, we propose an initialization algorithm that utilizes a small number of extra fully observed samples to produce such a coarse initial estimate. Finally, we theoretically analyze their performance and provide asymptotic statistical and computational guarantees.

    Original languageEnglish (US)
    Title of host publication35th International Conference on Machine Learning, ICML 2018
    EditorsAndreas Krause, Jennifer Dy
    PublisherInternational Machine Learning Society (IMLS)
    Pages6050-6070
    Number of pages21
    ISBN (Electronic)9781510867963
    StatePublished - Jan 1 2018
    Event35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden
    Duration: Jul 10 2018Jul 15 2018

    Publication series

    Name35th International Conference on Machine Learning, ICML 2018
    Volume9

    Other

    Other35th International Conference on Machine Learning, ICML 2018
    CountrySweden
    CityStockholm
    Period7/10/187/15/18

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    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Human-Computer Interaction
    • Software

    Cite this

    Nguyen, T. V., Soni, A., & Hegde, C. (2018). On learning sparsely used dictionaries from incomplete samples. In A. Krause, & J. Dy (Eds.), 35th International Conference on Machine Learning, ICML 2018 (pp. 6050-6070). (35th International Conference on Machine Learning, ICML 2018; Vol. 9). International Machine Learning Society (IMLS).