Corpus ID: 3353603

Nonconvex Matrix Factorization from Rank-One Measurements

@inproceedings{Li2019NonconvexMF,
  title={Nonconvex Matrix Factorization from Rank-One Measurements},
  author={Yuanxin Li and C. Ma and Y. Chen and Yuejie Chi},
  booktitle={AISTATS},
  year={2019}
}
  • Yuanxin Li, C. Ma, +1 author Yuejie Chi
  • Published in AISTATS 2019
  • Computer Science, Mathematics
    • We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural networks, among others. Our approach is to directly estimate the low-rank factor by minimizing a nonconvex quadratic loss function via vanilla gradient descent, following a tailored spectral initialization. When the true rank is small, this algorithm is… CONTINUE READING
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    32 Citations
    Highly Influencial Citations
    3
    Background Citations
    13
    Methods Citations
    9
    32 Citations
    Citation Type

    Citation Type

    Beyond Procrustes: Balancing-free Gradient Descent for Asymmetric Low-Rank Matrix Sensing
    • C. Ma, Yuanxin Li, Yuejie Chi
    • Computer Science, Engineering
    • 2019 53rd Asilomar Conference on Signals, Systems, and Computers
    • 2019
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    Nonconvex Low-Rank Matrix Recovery with Arbitrary Outliers via Median-Truncated Gradient Descent
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    Low-Rank Matrix Recovery with Scaled Subgradient Methods: Fast and Robust Convergence Without the Condition Number
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    Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descent
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    Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization
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    Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
    • 146
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    Noisy Matrix Completion : Understanding the Stability of Convex Relaxation via Nonconvex Optimization
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    Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence
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    Median-Truncated Gradient Descent: A Robust and Scalable Nonconvex Approach for Signal Estimation
    • 3
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    Harnessing Structures in Big Data via Guaranteed Low-Rank Matrix Estimation: Recent Theory and Fast Algorithms via Convex and Nonconvex Optimization
    • 68
    • PDF

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