Corpus ID: 231802094

On the computational and statistical complexity of over-parameterized matrix sensing

  title={On the computational and statistical complexity of over-parameterized matrix sensing},
  author={Jiacheng Zhuo and Jeongyeol Kwon and Nhat Ho and Constantine Caramanis},
We consider solving the low rank matrix sensing problem with Factorized Gradient Descend (FGD) method when the true rank is unknown and over-specified, which we refer to as over-parameterized matrix sensing. If the ground truth signal X∗ ∈ Rd∗d is of rank r, but we try to recover it using FF> where F ∈ Rd∗k and k > r, the existing statistical analysis falls short, due to a flat local curvature of the loss function around the global maxima. By decomposing the factorized matrix F into separate… Expand

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