Provable Subspace Tracking with Missing Entries

Narayanamurthy, Praneeth; Daneshpajooh, Vahid; Vaswani, Namrata

doi:10.1109/isit.2019.8849782

Cited by 1 publication

(2 citation statements)

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“…NORST-miss-rob GRASTA-RMC projected-GD 0.0832 (3) 0.1431 (2.9) 0.5699 (2) 10 −4 , ξ = x min /15, and ω supp = x min /2 = 5. We compare 5 GRASTA-RMC [49] and projected-GD [24].…”

Section: F Rst-miss and Rmcmentioning

confidence: 99%

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Provable Subspace Tracking From Missing Data and Matrix Completion

Narayanamurthy

Daneshpajooh

Vaswani

2019

IEEE Trans. Signal Process.

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We study the problem of subspace tracking in the presence of missing data (ST-miss). In recent work, we studied a related problem called robust ST. In this work, we show that a simple modification of our robust ST solution also provably solves ST-miss and robust ST-miss. To our knowledge, our result is the first "complete" guarantee for ST-miss. This means that we can prove that under assumptions on only the algorithm inputs, the output subspace estimates are close to the true data subspaces at all times. Our guarantees hold under mild and easily interpretable assumptions, and allow the underlying subspace to change with time in a piecewise constant fashion. In contrast, all existing guarantees for ST are partial results and assume a fixed unknown subspace. Extensive numerical experiments are shown to back up our theoretical claims. Finally, our solution can be interpreted as a provably correct mini-batch and memoryefficient solution to low rank Matrix Completion (MC).

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“…NORST-miss-rob GRASTA-RMC projected-GD 0.0832 (3) 0.1431 (2.9) 0.5699 (2) 10 −4 , ξ = x min /15, and ω supp = x min /2 = 5. We compare 5 GRASTA-RMC [49] and projected-GD [24].…”

Section: F Rst-miss and Rmcmentioning

confidence: 99%

“…ST-miss can be interpreted as an easier special case of robust ST (ST in the presence of additive sparse outliers) [3]. We also Parts of this paper will be presented at IEEE International Conference on Acoustics, Speech, and Signal Processing, 2019 [1] and IEEE International Symposium on Information Theory, 2019 [2].…”

Section: Introductionmentioning

confidence: 99%