Corpus ID: 3353603

Nonconvex Matrix Factorization from Rank-One Measurements

  title={Nonconvex Matrix Factorization from Rank-One Measurements},
  author={Yuanxin Li and C. Ma and Y. Chen and Yuejie Chi},
  • 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
    32 Citations
    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
    • 3
    • PDF
    Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
    • 146
    • PDF


    Low-Rank Positive Semidefinite Matrix Recovery From Corrupted Rank-One Measurements
    • 24
    • PDF
    Nonconvex Low-Rank Tensor Completion from Noisy Data
    • 16
    Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization
    • 39
    • PDF
    Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
    • 146
    • PDF
    Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guarantees
    • 217
    • PDF
    Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements
    • E. Candès, Y. Plan
    • Mathematics, Computer Science
    • IEEE Transactions on Information Theory
    • 2011
    • 460
    ROP: Matrix Recovery via Rank-One Projections
    • 105
    • PDF
    Kaczmarz Method for Solving Quadratic Equations
    • 36
    • PDF
    Exact and Stable Covariance Estimation From Quadratic Sampling via Convex Programming
    • 167
    • PDF