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We show that solutions to the popular convex matrix LASSO problem (nuclear-norm--penalized linear least-squares) have low rank under similar assumptions as required by classical low-rank matrix sensing error bounds.
New York: Springer, 1997
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L. Ding, L. Jiang, Y. Chen, Q. Qu, and Z. Zhu, “Rank overspecified robust matrix recovery: Subgradient method and exact recovery,” in Proc. Conf. Neural Inf. Process. Syst. (NeurIPS)
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2018
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R. Y. Zhang, C. Josz, S. Sojoudi, and J. Lavaei, “How much restricted isometry is needed in nonconvex matrix recovery?,” in Proc. Conf. Neural Inf. Process. Syst. (NeurIPS)
2018
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J. Sun, Q. Qu, and J. Wright, “A geometric analysis of phase retrieval,” Found. Comput. Math
2018
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Z. Zhu, Q. Li, G. Tang, and M. B. Wakin, “Global optimality in low-rank matrix optimization,” IEEE Trans. Signal Process
2018
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X. Zhang, L. Wang, Y. Yu, and Q. Gu, “A primal-dual analysis of global optimality in nonconvex low-rank matrix recovery,” in Proc. Int. Conf. Mach. Learn. (ICML)
2018
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A. B. Taylor, J. M. Hendrickx, and F. Glineur, “Exact worst-case convergence rates of the proximal gradient method for composite convex minimization,” J. Opt. Theory Appl
2018
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2019
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L. T. Nguyen, J. Kim, and B. Shim, “Low-rank matrix completion: A contemporary survey,” IEEE Access
2019
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2021
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Y. Bi and J. Lavaei, “On the absence of spurious local minima in nonlinear low-rank matrix recovery problems,” in Proc. Int. Conf. Artif. Intell. Statist. (AISTATS)
2021
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2022
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2022
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Z. Ma, Y. Bi, J. Lavaei, and S. Sojoudi, “Sharp restricted isometry property bounds for low-rank matrix recovery problems with corrupted measurements,” in Proc. AAAI Conf. Artif. Intell. (AAAI)
2022
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Y. Luo and N. G. Trillos, “Nonconvex matrix factorization is geodesically convex: Global landscape analysis for fixed-rank matrix optimization from a Riemannian perspective,” Sept. 2022
2022
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J. Ma and S. Fattahi, “Global convergence of sub-gradient method for robust matrix recovery: Small initialization, noisy measurements, and over-parameterization,” J. Mach. Learn. Res
2023
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Y. Chen, J. Fan, B. Wang, and Y. Yan, “Convex and nonconvex optimization are both minimax-optimal for noisy blind deconvolution under random designs,” J. Amer. Stat. Assoc
2023
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H. Zhang, B. Yalçın, J. Lavaei, and S. Sojoudi, “A new complexity metric for nonconvex rank-one generalized matrix completion,” Math. Program
2023
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J. Ma and S. Fattahi, “Can learning be explained by local optimality in low-rank matrix recovery?,” Feb. 2023
2023
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Z. Ma and S. Sojoudi, “Noisy low-rank matrix optimization: Geometry of local minima and convergence rate,” in Proc. Int. Conf. Artif. Intell. Statist. (AISTATS)
2023
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Z. Ma, Y. Bi, J. Lavaei, and S. Sojoudi, “Geometric analysis of noisy low-rank matrix recovery in the exact parametrized and the overparametrized regimes,” INFORMS J. Opt
2023
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R. Y. Zhang, “Improved global guarantees for the nonconvex Burer-Monteiro factorization via rank overparameterization,” Math. Program
2024
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N. Boumal and A. D. McRae, “The usual smooth lift of the nuclear norm regularizer enjoys 2 ⇒ 1 2\Rightarrow 1 ,” Oct. 2024
2024
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