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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
The nature of these phase transitions and associated universality classes remain incompletely understood.  ...  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

Unsupervised learning of control signals and their encodings in C. elegans whole-brain recordings [article]

Charles Fieseler, Manuel Zimmer, J. Nathan Kutz
2020 arXiv   pre-print
These control signals are shown to be implicated in transitions between behaviors.  ...  This method learns the control signals in an unsupervised way from data, then uses Dynamic Mode Decomposition with control (DMDc) to create the first global, linear dynamical system that can reconstruct  ...  An alternate method uses different phase loops and the phase along them to predict behavior, producing conserved dynamics in a special phase space [14] .  ... 
arXiv:2001.08346v3 fatcat:doyar44ssrafbjowrbirpduyrq

Statistical Mechanics of Compressed Sensing

Surya Ganguli, Haim Sompolinsky
2010 Physical Review Letters  
We find surprising and useful regularities in the nature of errors made by CS, a new phase transition which reveals the possibility of CS for nonnegative signals without optimization, and a new null model  ...  for sparse regression.  ...  The theory gives a remarkably simple, universal prediction for this quantity that is independent of Pðx 0 Þ: in the perfect reconstruction phase, L 0 ð xÞ ¼ f independent of , and in the error phase, L  ... 
doi:10.1103/physrevlett.104.188701 pmid:20482215 fatcat:vsgp2ufl5vaoxo3nqbi25l7co4

SparseBeads data: benchmarking sparsity-regularized computed tomography

Jakob S Jørgensen, Sophia B Coban, William R B Lionheart, Samuel A McDonald, Philip J Withers
2017 Measurement science and technology  
A collection of 48 x-ray CT datasets called SparseBeads was designed for benchmarking SR reconstruction algorithms.  ...  and noise levels to allow the systematic assessment of parameters affecting performance of SR reconstruction algorithms 6 .  ...  In [28] a sharp phase transition was observed empirically for TV-regularized reconstruction of a class of images with sparse gradient magnitude.  ... 
doi:10.1088/1361-6501/aa8c29 fatcat:yxrowldk4fhtvfrunukqsofcme

Determination of Nonlinear Genetic Architecture using Compressed Sensing [article]

Chiu Man Ho, Stephen D.H. Hsu
2015 arXiv   pre-print
An example of a sparse nonlinear model is one in which a typical locus interacts with several or even many others, but only a small subset of all possible interactions exist.  ...  We give theoretical arguments suggesting that the method is nearly optimal in performance, and demonstrate its effectiveness on broad classes of nonlinear genetic models using both real and simulated human  ...  This work is supported in part by funds from the Office of the Vice-President for Research and Graduate Studies at Michigan State University.  ... 
arXiv:1408.6583v2 fatcat:db6rbyhbuzbntb5o6wi4wkmohi

Optimal Phase Transitions in Compressed Sensing

Yihong Wu, Sergio Verdu
2012 IEEE Transactions on Information Theory  
The optimal phase-transition threshold is determined as a functional of the input distribution and compared to suboptimal thresholds achieved by popular reconstruction algorithms.  ...  Focusing on optimal decoders, we investigate the fundamental tradeoff between measurement rate and reconstruction fidelity gauged by error probability and noise sensitivity in the absence and presence  ...  VI-A]), resulting in the phase-transition threshold and for sparse positive and simple signals, given by (86) and (87), respectively.  ... 
doi:10.1109/tit.2012.2205894 fatcat:sqfxlxfrbvfexajzmog3e7d42i

Determination of nonlinear genetic architecture using compressed sensing

Chiu Man Ho, Stephen DH Hsu
2015 GigaScience  
A phase transition (i.e., dramatic and qualitative change) in the behavior of the algorithm indicates when sufficient data is available for its successful application.  ...  An example of a sparse nonlinear model is one in which a typical locus interacts with several or even many others, but only a small subset of all possible interactions exist.  ...  This work is supported in part by funds from the Office of the Vice-President for Research and Graduate Studies at Michigan State University.  ... 
doi:10.1186/s13742-015-0081-6 pmid:26380078 pmcid:PMC4570224 fatcat:a5nsmagtebeulh3pjnznlstyre

Fast Solution of $\ell _{1}$-Norm Minimization Problems When the Solution May Be Sparse

David L. Donoho, Yaakov Tsaig
2008 IEEE Transactions on Information Theory  
When this property holds and k is small compared to the problem size, this means that 1 minimization problems with k-sparse solutions can be solved in a fraction of the cost of solving one full-sized linear  ...  Our approach also sheds light on the evident parallelism in results on 1 minimization and Orthogonal Matching Pursuit (OMP), and aids in explaining the inherent relations between Homotopy, LARS, OMP, and  ...  We now describe an objective framework for estimating phase transitions from simulation data.  ... 
doi:10.1109/tit.2008.929958 fatcat:6fs7h3zirraybowx2q6vzv2eia

Sampling limits for electron tomography with sparsity-exploiting reconstructions

Yi Jiang, Elliot Padgett, Robert Hovden, David A. Muller
2018 Ultramicroscopy  
Popularized by compressed sensing, sparsity-exploiting algorithms have been applied to experimental ET data and show promise for improving reconstruction quality or reducing the total beam dose applied  ...  Moreover, a limited tilt range of +-75 or less can result in distorting artifacts in sparsity-exploiting reconstructions. The influence of optimization parameters on reconstructions is also discussed.  ...  Xiaochuan Pan from the University of Chicago for many helpful discussions. The tomviz project is supported by DOE Office of Science contract DE-SC0011385.  ... 
doi:10.1016/j.ultramic.2017.12.010 pmid:29277084 fatcat:wtm2m2f7srabjdp5nffj55ceqe

Machine Learning Methods for Attack Detection in the Smart Grid

Mete Ozay, Inaki Esnaola, Fatos Tunay Yarman Vural, Sanjeev R. Kulkarni, H. Vincent Poor
2016 IEEE Transactions on Neural Networks and Learning Systems  
An attack detection framework is provided to exploit any available prior knowledge about the system and surmount constraints arising from the sparse structure of the problem in the proposed approach.  ...  Attack detection problems in the smart grid are posed as statistical learning problems for different attack scenarios in which the measurements are observed in batch or online settings.  ...  However, the phase transitions occur before the critical values, and the values of the phase transition points decrease as the system size increases.  ... 
doi:10.1109/tnnls.2015.2404803 pmid:25807571 fatcat:lx4y76clavei5lfvbiqrvgqavi

Abnormal Event Detection and Location for Dense Crowds using Repulsive Forces and Sparse Reconstruction [article]

Pei Lv, Shunhua Liu, Mingliang Xu, Bing Zhou
2018 arXiv   pre-print
This paper proposes a method based on repulsive forces and sparse reconstruction for the detection and location of abnormal events in crowded scenes.  ...  To further improve the detection efficiency and avoid concept drift, we propose a fully unsupervised global and local dynamic updating algorithm, based on sparse reconstruction and a group of word pools  ...  Finally, to solve the problems of degradation and concept drift in dictionaries, we propose an unsupervised learning and updating algorithm for the group dictionary model based on sparse reconstruction  ... 
arXiv:1808.06749v1 fatcat:med4kfc7tbdjlicpt3ymvfc46u

Topology-Induced Inverse Phase Transitions [article]

D. De Martino, S. Bradde, L. Dall'Asta, M. Marsili
2012 arXiv   pre-print
Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling.  ...  We show it both analytically and numerically, providing also a microscopic interpretation of inverse transitions in terms of freezing of sparse subgraphs and coupling renormalization.  ...  In summary, the CW approximation would suggest that in the BC model an inverse phase transition can be triggered by a different scaling of first and second order critical lines with the moments of the  ... 
arXiv:1010.4062v2 fatcat:24fumbgg4jcfhknlcxmfafsvie

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
It will then spread as a "reconstruction wave" similar to the crystal in the water. After an introduction to statistical inference and sparse linear estimation, we will introduce the necessary tools.  ...  This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems.  ...  The divergence of the convergence time of AMP approaching the phase transitions is the critical slowing down discussed in sec. 5.1.1, a typical behavior of local algorithms near first order phase transitions  ... 
arXiv:1511.01650v1 fatcat:iusrdds7yrcpfegqqjlslyy2bm

Graph Learning Under Partial Observability [article]

Vincenzo Matta, Augusto Santos, Ali H. Sayed
2020 arXiv   pre-print
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling  ...  In this article, we examine the inverse problem and consider the reverse question: How much information does observing the behavior at the nodes of a graph convey about the underlying topology?  ...  The logarithmic growth corresponds i phase transition, in the sense that is the minimal ensures a connected graph.  ... 
arXiv:1912.08465v3 fatcat:atbnrw4onfayrcdxm6yzpomt34

A Review of Complex Systems Approaches to Cancer Networks [article]

Abicumaran Uthamacumaran
2020 arXiv   pre-print
Machine learning, network science and algorithmic information dynamics are discussed as current tools for cancer network reconstruction.  ...  Deep Learning architectures and computational fluid models are proposed for better forecasting gene expression patterns in cancer ecosystems.  ...  The criticality of GRNs has been discussed as fluctuating at the phase-transition point between ordered and chaotic regimes for the dynamics of those networks.  ... 
arXiv:2009.12693v2 fatcat:kt3e4bqaufgwlbhx2wbgzftnpe
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