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| Presentation | 2014-11-21 12:15 Dynamics of compressed sensing at zero temperature Jun-ichi Inoue (Hokkaido Univ.)  NC2014-29 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | We discuss dynamics of signal restoring process in compressed sensing based on the $L_{r}$-minimizer. In particular, we will focus on the dynamics at `zero temperature', which means that we utilize the MAP estimate for the solution by gradient descent learning of the cost function (logarithm of the posterior). When we regard the number of sampling as `the number of examples', and the original signal to be reconstructed as `synaptic weight vector', the dynamics of compressed sensing could be treated as a sort of `learning from examples'. In this paper, we examine the case of $r=2$. Then, we find that the steady state of estimated signal vector by means of the gradient descent learning is written in terms of the pseudo inverse matrix, which has been well-known in the literature of `AdaLine (Adaptive Linear Neuron) learning' for artificial neural networks. In order to evaluate the average-case performance of reconstruction dynamics, we derive coarse-grained dynamics with respect to several macroscopic quantities. We find that the dynamics contains an eigenvalue spectrum for correlation matrix whose elements are constructed by observation matrix. For the simplest choice of ensemble of observation matrix, we calculate the explicit form of the eigenvalue distribution and discuss the learning rate and hyper-parameter dependences of the mean-square error, and we also argue the residual error as a function of sparse and sampling rates. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Compressed sensing / Signal reconstruction dynamics / Learning theory / Random matrix theory / Average-case performance / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 114, no. 326, NC2014-29, pp. 21-26, Nov. 2014. | |
| Paper # | NC2014-29 | |
| Date of Issue | 2014-11-14 (NC) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | NC2014-29 |
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| Conference Information | |
| Committee | MBE NC |
| Conference Date | 2014-11-21 - 2014-11-22 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Tohoku University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | NC |
| Conference Code | 2014-11-MBE-NC |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Dynamics of compressed sensing at zero temperature |
| Sub Title (in English) | |
| Keyword(1) | Compressed sensing |
| Keyword(2) | Signal reconstruction dynamics |
| Keyword(3) | Learning theory |
| Keyword(4) | Random matrix theory |
| Keyword(5) | Average-case performance |
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| 1st Author's Name | Jun-ichi Inoue |
| 1st Author's Affiliation | Hokkaido University (Hokkaido Univ.) |
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| Speaker | Author-1 |
| Date Time | 2014-11-21 12:15:00 |
| Presentation Time | 25 minutes |
| Registration for | NC |
| Paper # | NC2014-29 |
| Volume (vol) | vol.114 |
| Number (no) | no.326 |
| Page | pp.21-26 |
| #Pages | 6 |
| Date of Issue | 2014-11-14 (NC) |
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