Entropy Estimates on Tensor Products of Banach Spaces and Applications to Low-Rank Recovery

Lee, Kiryung; Srinivasa, Rakshith Sharma; Junge, Marius; Romberg, Justin

doi:10.1109/sampta45681.2019.9030989

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Completion Of Bounded and Approximately Low-rank Matrices1

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2021

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“…Therefore, to get an upper bound in (22), it suffices to calculate the moments of E 2,1 pvq and }v}.…”

Section: Completion Of Bounded and Approximately Low-rank Matricesmentioning

confidence: 99%

Approximately low-rank recovery from noisy and local measurements by convex program

Lee¹,

Srinivasa²,

Junge³

et al. 2021

Preprint

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Low-rank matrix models have been universally useful for numerous applications starting from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low-rankness has a nice analogy with the ℓ 1 norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensornorm-constrained estimator for recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regulizer is designed adapting to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching through applying Maurey's empirical method to tensor products of Banach spaces. The estimator provides a near optimal error bound in a minimax sense and admits a polynomial-time algorithm for these applications.

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“…Therefore, to get an upper bound in (22), it suffices to calculate the moments of E 2,1 pvq and }v}.…”

Section: Completion Of Bounded and Approximately Low-rank Matricesmentioning

confidence: 99%

Approximately low-rank recovery from noisy and local measurements by convex program

Lee¹,

Srinivasa²,

Junge³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Entropy Estimates on Tensor Products of Banach Spaces and Applications to Low-Rank Recovery

Cited by 1 publication

References 16 publications

Approximately low-rank recovery from noisy and local measurements by convex program

Approximately low-rank recovery from noisy and local measurements by convex program

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