Ramesh, L and Murthy, CR and Tyagi, H (2019) Sample-Measurement Tradeoff in Support Recovery Under a Subgaussian Prior. In: 2019 IEEE International Symposium on Information Theory, ISIT 2019, 7 - 12 July 2019, Paris, pp. 2709-2713.
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Abstract
Data samples from Rd with a common support of size k are accessed through m random linear projections (measurements) per sample. It is well-known that roughly k measurements from a single sample are sufficient to recover the support. In the multiple sample setting, do k overall measurements still suffice when only m measurements per sample are allowed, with m < k? We answer this question in the negative by considering a generative model setting with independent samples drawn from a subgaussian prior. We show that n= Θ ((k2/m2) · log k(d-k)) samples are necessary and sufficient to recover the support exactly. In turn, this shows that when m < k, k overall measurements are insufficient for support recovery; instead we need about m measurements each from k2/m2 samples, and therefore k2/m overall measurements are necessary. © 1963-2012 IEEE.
| Item Type: | Conference Paper |
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| Publication: | IEEE International Symposium on Information Theory - Proceedings |
| Publisher: | Institute of Electrical and Electronics Engineers Inc. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Information theory, Closed-form expression; Data sample; Generative model; Independent samples; Linear projections; Optimal estimator; Sub-Gaussians; Support recoveries, Recovery |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 19 Oct 2022 10:49 |
| Last Modified: | 19 Oct 2022 10:49 |
| URI: | https://eprints.iisc.ac.in/id/eprint/77496 |
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