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Phase Transitions for Support Recovery from Gaussian Linear Measurements

Ramesh, L and Murthy, CR and Tyagi, H (2021) Phase Transitions for Support Recovery from Gaussian Linear Measurements. In: 2021 IEEE International Symposium on Information Theory, ISIT 2021, 12-20 Jul 2021, Melbourne, pp. 1606-1611.

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Official URL: https://doi.org/10.1109/ISIT45174.2021.9518252


We study the problem of recovering the common k-sized support of a set of n samples of dimension d, using m noisy linear measurements per sample. Most prior work has focused on the case when m exceeds k, in which case n of the order (k/m)łog(d/k) is both necessary and sufficient. Thus, in this regime, only the total number of measurements across the samples matter, and there is not much benefit in getting more than k measurements per sample. In the measurement-constrained regime where we have access to fewer than k measurements per sample, we show an upper bound of O((k²/m²)łog d) on the sample complexity for successful support recovery when m\geq 2łog d. Along with the lower bound from our previous work, this shows a phase transition for the sample complexity of this problem around k/m=1. In fact, our proposed algorithm is sample-optimal in both the regimes. It follows that, in the młl k regime, multiple measurements from the same sample are more valuable than measurements from different samples. © 2021 IEEE.

Item Type: Conference Paper
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 Institute of Electrical and Electronics Engineers Inc.
Keywords: Information theory, Gaussians; Linear measurements; Lower bounds; Multiple measurements; Sample complexity; Support recoveries; Upper Bound, Recovery
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 03 Dec 2021 08:40
Last Modified: 03 Dec 2021 08:40
URI: http://eprints.iisc.ac.in/id/eprint/70260

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