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Critical behavior and universality classes for an algorithmic phase transition in sparse reconstruction [article]

Mohammad Ramezanali, Partha P. Mitra, Anirvan M. Sengupta
2015 arXiv   pre-print
We analyze the mean field equations from the cavity method for two sparse reconstruction algorithms, Basis Pursuit and Elastic Net.  ...  In the limit λ→ 0 and N→∞, keeping ρ=K/N fixed, exact recovery is possible for sufficiently large values of fractional measurement number α=M/N, with an algorithmic phase transition occurring at a known  ...  The final version of this paper was written while two of the authors (AMS and MR) were visiting Simons Center for Data Analysis at Simons Foundation. We are grateful for their hospitality.  ... 
arXiv:1509.08995v2 fatcat:mxnprfu6uneubnnbb2gihdqtgq

Message passing algorithms for the Hopfield network reconstruction: Threshold behavior and limitation

Haiping Huang
2010 Physical Review E  
On the other hand, a threshold behavior is observed for the susceptibility propagation algorithm and the transition from good reconstruction to poor one becomes sharper as the network size increases.  ...  Its performance deteriorates as the data becomes highly magnetized, and this method finally fails in the presence of the frozen type data where at least two of its magnetizations are equal to one in absolute  ...  The present work was in part supported by the National Science Foundation of China (Grant No. 10774150) and by the National Basic Research  ... 
doi:10.1103/physreve.82.056111 pmid:21230549 fatcat:3gtrfma3yncffohcsapkgvh3au

Compressed sensing under matrix uncertainty: Optimum thresholds and robust approximate message passing

Florent Krzakala, Marc Mezard, Lenka Zdeborova
2013 2013 IEEE International Conference on Acoustics, Speech and Signal Processing  
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal.  ...  Here we present two contributions to this problem: first, we use the replica method to determine the mean-squared error of the Bayes-optimal reconstruction of sparse signals under matrix uncertainty.  ...  CONCLUSIONS We have computed the Bayes-optimal value of the MSE for the reconstruction of sparse Gauss-Bernoulli signals in presence of matrix uncertainty with the replica method, and consider a variant  ... 
doi:10.1109/icassp.2013.6638719 dblp:conf/icassp/KrzakalaMZ13 fatcat:cjh7v3qw4jd4ngfcrddxopeqqq

Finding One Community in a Sparse Graph

Andrea Montanari
2015 Journal of statistical physics  
In this paper we present two sets of contributions: (i) We use the cavity method from spin glass theory to derive an exact phase diagram for the reconstruction problem.  ...  For small hidden sets and large average degree, the phase transition for local algorithms takes an intriguingly simple form.  ...  Phase transitions via cavity method In this section we use the cavity method to derive an exact phase diagram of the model.  ... 
doi:10.1007/s10955-015-1338-2 fatcat:iyr2g7ezpzd6xhhvxmnr7pvzne

Information-Theoretic Bounds and Phase Transitions in Clustering, Sparse PCA, and Submatrix Localization

Jess Banks, Cristopher Moore, Roman Vershynin, Nicolas Verzelen, Jiaming Xu
2018 IEEE Transactions on Information Theory  
For sparse PCA and submatrix localization, we determine this threshold exactly in the limit where the number of blocks is large or the signal matrix is very sparse; for the clustering problem, our bounds  ...  This regime is analogous to the conjectured 'hard but detectable' regime for community detection in sparse graphs. J. Banks is with the  ...  technique and cavity method.  ... 
doi:10.1109/tit.2018.2810020 fatcat:djasi4gkhrb2rk6ochxgec3gwa

Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization

Jess Banks, Cristopher Moore, Roman Vershynin, Nicolas Verzelen, Jiaming Xu
2017 2017 IEEE International Symposium on Information Theory (ISIT)  
For sparse PCA and submatrix localization, we determine this threshold exactly in the limit where the number of blocks is large or the signal matrix is very sparse; for the clustering problem, our bounds  ...  This regime is analogous to the conjectured 'hard but detectable' regime for community detection in sparse graphs. J. Banks is with the  ...  technique and cavity method.  ... 
doi:10.1109/isit.2017.8006706 dblp:conf/isit/BanksMVVX17 fatcat:6n7hc2hjbrehviy52ddwsvx2ou

Statistical physics and approximate message-passing algorithms for sparse linear estimation problems in signal processing and coding theory [article]

Jean Barbier
2015 arXiv   pre-print
The main tools are the graphical models and approximate message-passing algorithm together with the cavity method.  ...  This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems.  ...  In gradient-optimization-based methods for image reconstruction, instead of searching for a sparse signal in the pixel domain as in (8.2), we seek for a signal with a sparse discrete gradient.  ... 
arXiv:1511.01650v1 fatcat:iusrdds7yrcpfegqqjlslyy2bm

Exact asymptotics for phase retrieval and compressed sensing with random generative priors [article]

Benjamin Aubin, Bruno Loureiro, Antoine Baker, Florent Krzakala, Lenka Zdeborová
2020 arXiv   pre-print
We compare the performance to sparse separable priors and conclude that generative priors might be advantageous in terms of algorithmic performance.  ...  We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm for an ensemble of generative priors consisting of fully connected deep neural  ...  We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp GPU used for this research.  ... 
arXiv:1912.02008v2 fatcat:m5u7cq6zpbgcln432gsk3kyjbq

Phase transitions in community detection: A solvable toy model

Greg Ver Steeg, Cristopher Moore, Aram Galstyan, Armen Allahverdyan
2014 Europhysics letters  
This transition was first computed using the cavity method, and has been proved rigorously in the case of q=2 groups.  ...  Recently, it was shown that there is a phase transition in the community detection problem.  ...  Acknowledgments A.G. and G.V.S. thank the Santa Fe Institute for their hospitality.  ... 
doi:10.1209/0295-5075/106/48004 fatcat:mmcifbw6fzfa3jbe5ld44vg6lm

Application of ultrasound molecular imaging based on compressed sensing reconstruction algorithm to phase change drug-loaded PLGA nanoparticles targeting breast cancer MCF-7 Cells

Yufeng You, Wusong Cheng, Hongbo Chen
2021 Pakistan Journal of Medical Sciences  
Objectives: To study the ability of aptamer-modified nano-gold rods and liquid carbon-targeted PLGA nanoparticles to target in vitro using compressed sensing reconstruction algorithm, and observe the phenomenon  ...  Application of ultrasound molecular imaging based on compressed sensing reconstruction algorithm to phase change drug-loaded PLGA nanoparticles targeting breast cancer MCF-7 Cells.  ...  Compressed sensing reconstruction algorithm: Compressed sensing is a new information acquisition theory.  ... 
doi:10.12669/pjms.37.6-wit.4852 pmid:34712292 pmcid:PMC8520378 fatcat:ijrg2s5xq5a5lmholbhbre2rde

Typology of phase transitions in Bayesian inference problems

Federico Ricci-Tersenghi, Guilhem Semerjian, Lenka Zdeborová
2019 Physical review. E  
We support this discussion by quantitative expansions of the functional cavity equations that describe inference problems on sparse graphs.  ...  Our results show that the instability of the trivial fixed point is not a generic evidence for the Bayes-optimality of the message passing algorithms.  ...  for discussions about bifurcation phase diagrams.  ... 
doi:10.1103/physreve.99.042109 fatcat:4whnqjns6baj3odandczn3m5cy

Sparse signal reconstruction based on experimental chaos generated by a laser diode

D. Rontani, D. Choi, C.-Y. Chang, A. Locquet, D. S. Citrin, Krassimir Panajotov, Marc Sciamanna, Angel Valle, Rainer Michalzik
2016 Semiconductor Lasers and Laser Dynamics VII  
Specifically, we find that a wide range of the laser operational parameters and dynamical complexity guarantees that the generation of a sensing matrix, necessary for sparse reconstruction, has a comparable  ...  Our result opens new avenues for the use of optical chaotic devices for signal processing applications at ultra-high speed.  ...  The results are shown in Figure 4 . We observe that in both cases the transition toward poor reconstruction performance occurs for a similar sparsity level, around K=15.  ... 
doi:10.1117/12.2227633 fatcat:cax4x5k3ffgpfpnegqlblf32vm

The cavity method for analysis of large-scale penalized regression [article]

Mohammad Ramezanali, Partha P. Mitra, Anirvan M. Sengupta
2015 arXiv   pre-print
For large-scale problems, these algorithms exhibit sharp phase transition boundaries where sparse retrieval breaks down.  ...  Unfortunately, the replica trick and the non-trivial zero temperature limit obscure the underlying reasons for the failure of a sparse reconstruction algorithm, and of penalized regression methods, in  ...  We find that for the problem at hand, the cavity method provides better insight in comparison to the replica formalism and has the potential to lead to substantially better sparse reconstruction algorithms  ... 
arXiv:1501.03194v2 fatcat:3qicnhkv45bafaa3znogtg2zjm

Parallel tempering for the planted clique problem

Angelini Maria Chiara
2018 Journal of Statistical Mechanics: Theory and Experiment  
In this paper we will apply a standard method for the analysis of disordered models, the Parallel-Tempering (PT) algorithm, to the clique problem, showing numerically that its time-scaling in the hard  ...  Also in this case PT shows a polynomial scaling in the hard region for the recovery.  ...  Averages are performed over 1000 sample for N = 1000 and 300 samples for N = 10000, 20000.that is in the hard phase for the reconstruction of the planted solution.  ... 
doi:10.1088/1742-5468/aace2c fatcat:imkjgiw2jnclbn3ggxbqb46bie

Sparse-TFM Imaging of Lamb Waves for the Near-Distance Defects in Plate-Like Structures

Haiyan Zhang, Yaqun Liu, Guopeng Fan, Hui Zhang, Wenfa Zhu, Qi Zhu
2019 Metals  
In order to improve the imaging resolution, the location of active array elements in the sparse array can be optimized using the genetic algorithm (GA).  ...  A sparse-TFM algorithm is adopted in this work to solve the problem regarding rapid imaging of near- distance defects in thin plates.  ...  Some researchers even called TFM the "golden rule" algorithm in ultrasonic phased array testing.  ... 
doi:10.3390/met9050503 fatcat:bj5u7t6y5fepdavpxhrpai32ke
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