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.
PDF
ISIT_1606-1611_2021.pdf - Published Version Restricted to Registered users only Download (383kB) | Request a copy |
Abstract
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 |
Actions (login required)
View Item |