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Two-level preconditioning for Ridge Regression [article]

Joris Tavernier, Jaak Simm, Karl Meerbergen, Yves Moreau
2020 arXiv   pre-print
Here, we develop a two-level preconditioner for regularized least squares linear systems involving a feature or data matrix.  ...  We observed speed-ups for artificial and real-life data.  ...  We would additionally like to thank David Vanavermaete for generating the SNP data sets.  ... 
arXiv:1806.05826v2 fatcat:webaz3x35fbjhhgufaodzssjyy

An improved FOCUSS-based learning algorithm for solving sparse linear inverse problems

J.F. Murray, K. Kreutz-Delgado
2001 Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256)  
We develop an improved algorithm for solving blind sparse linear inverse problems where both the dictionary (possibly overcomplete) and the sources are unknown.  ...  This formulation leads to a constrained and regularized minimization problem which can be solved in part using the FOCUSS (Focal Underdetermined System Solver) algorithm for vector selection.  ...  The Focal Underdetermined System Solver (FOCUSS) was designed to solve for sparse solutions of linear inverse problems when is known [12, 6] , and performs the vector selection step of the algorithm.  ... 
doi:10.1109/acssc.2001.986949 fatcat:l6u3iu3d6jhbbfca6dewwv3qpe

Entropy Penalized Semidefinite Programming [article]

Mikhail Krechetov, Jakub Marecek, Yury Maximov, Martin Takac
2018 arXiv   pre-print
We show that EP-SDP problems admit efficient numerical algorithm having (almost) linear time complexity of the gradient iteration which makes it useful for many machine learning and optimization problems  ...  In this paper, we propose Entropy Penalized Semi-definite programming (EP-SDP) which provides a unified framework for a wide class of penalty functions used in practice to promote a low-rank solution.  ...  Data: Quadratic matrix S stands for the MAP Inference problem, staring point λ 0 , γ > 1, step size policy {η k } k≥1 accuracy parameters ε, ǫ Result: Solution V * stands for the local minimum of (EP-SDP  ... 
arXiv:1802.04332v3 fatcat:k6l3tvt53zhxvncw55svxksa4m

Multiscale Unbiased Diffeomorphic Atlas Construction on Multi-GPUs [chapter]

Linh Ha, Jens Krüger, Sarang Joshi, Cláudio T. Silva
2011 GPU Computing Gems Emerald Edition  
In this chapter, we present a high performance multi-scale 3D image processing framework to exploit the parallel processing power of multiple graphic processing units (Multi-GPUs) for medical image analysis  ...  We developed GPU algorithms and data structures that can be applied to a wide range of 3D image processing applications and efficiently exploit the computational power and massive bandwidth offered by  ...  Specially thank to Sam Preston, Marcel Prastawa and Thomas Fogal for their time and feedback on the work.  ... 
doi:10.1016/b978-0-12-384988-5.00048-6 fatcat:kl7jtl6dw5d5ngcdpgxpxv3p7q

A Confidence-based Iterative Solver of Depths and Surface Normals for Deep Multi-view Stereo [article]

Wang Zhao, Shaohui Liu, Yi Wei, Hengkai Guo, Yong-Jin Liu
2022 arXiv   pre-print
The key to our approach is a novel solver that iteratively solves for per-view depth map and normal map by optimizing an energy potential based on the locally planar assumption.  ...  This solver is not only effective as a post-processing tool for plane-based depth refinement and completion, but also differentiable such that it can be efficiently integrated into deep learning pipelines  ...  Bottom row: output depth after applying the proposed solver. cally, we apply the iterative solver over the depth map acquired from the sparse reconstruction of COLMAP [40, 41] .  ... 
arXiv:2201.07609v1 fatcat:6worss5hcvcltokpxxmk4axp5y

How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification [article]

Abd AlRahman R. AlMomani, Jie Sun, Erik Bollt
2019 arXiv   pre-print
Our method adopts an information-theoretic measure for the data-driven discovery of the underlying dynamics.  ...  We provide a numerical comparison with the current state-of-the-art methods in sparse regression, and we apply the methods to different chaotic systems such as the Lorenz System, the Kuramoto-Sivashinsky  ...  (Right) For a selected node, we see that it is basically influenced by few other nodes. SI.18: ER solution sparse representation for the coupled Logistic map created by Eqs.  ... 
arXiv:1905.08061v2 fatcat:ox76lj2n6ffo7abphmgntl7zqq

Efficient Preconditioners for a Shock Capturing Space-Time Discontinuous Galerkin Method for Systems of Conservation Laws

Andreas Hiltebrand, Siddhartha Mishra
2015 Communications in Computational Physics  
In this paper, we design efficient preconditioners for the large, non-symmetric linear system, that needs to be solved at every Newton step.  ...  AbstractAn entropy stable fully discrete shock capturing space-time Discontinuous Galerkin (DG) method was proposed in a recent paper to approximate hyperbolic systems of conservation laws.  ...  In turn, the Newton solver requires the solution of a linear system at every Newton sub-step. This linear system is very large, sparse and non-symmetric.  ... 
doi:10.4208/cicp.140214.271114a fatcat:4koxwpmezza6padarjcrsy6vjy

A Sparse Grid Based Generative Topographic Mapping for the Dimensionality Reduction of High-Dimensional Data [chapter]

Michael Griebel, Alexander Hullmann
2014 Modeling, Simulation and Optimization of Complex Processes - HPSC 2012  
We will show how a discretization based on sparse grids can be employed for the mapping between latent space and data space.  ...  The generative topographic mapping (GTM) finds a lower-dimensional parameterization for the data and thus allows for nonlinear dimensionality reduction.  ...  Instead, we use sparse grids [6] for the discretization of the mapping between latent space and data space.  ... 
doi:10.1007/978-3-319-09063-4_5 dblp:conf/hpsc/GriebelH12 fatcat:cpyortc63rhqzlypxpq2h5xkti

Multi-subject MEG/EEG source imaging with sparse multi-task regression

Hicham Janati, Thomas Bazeille, Bertrand Thirion, Marco Cuturi, Alexandre Gramfort
2020 NeuroImage  
Our analysis of a multimodal dataset shows how multi-subject source localization reduces the gap between MEG and fMRI for brain mapping.  ...  Although it can be cast as a linear regression, this problem is severely ill-posed as the number of observations, which equals the number of sensors, is small.  ...  As discussed in the introduction, standard sparse source localization solvers are 230 applied to the data of each subject independently.  ... 
doi:10.1016/j.neuroimage.2020.116847 pmid:32438046 fatcat:4zycfenpvnekzltdhhcqpoakm4

Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization [article]

Nir Shlezinger, Yonina C. Eldar, Stephen P. Boyd
2022 arXiv   pre-print
Model-based optimization and data-centric deep learning are often considered to be distinct disciplines.  ...  Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable optimization.  ...  Here the data was modeled as comprising a low-rank clutter background and a sparse blood flow image depicting the contrast agents.  ... 
arXiv:2205.02640v1 fatcat:rbt26xz3mngjjh4gcvjcs4p6ou

Fully Learnable Model for Task-Driven Image Compressed Sensing

Bowen Zheng, Jianping Zhang, Guiling Sun, Xiangnan Ren
2021 Sensors  
The Solver calculates the image's low-dimensional representation with the measurements. The Rebuilder learns a mapping from the low-dimensional latent space to the image space.  ...  All the mentioned could be trained jointly or individually for a range of application scenarios. The pre-trained FLCS reconstructs images with few iterations for task-driven compressed sensing.  ...  Acknowledgments: The authors would like to thank Tianjin Key Laboratory of Optoelectronic Sensor and Sensor Network Technology for providing working conditions.  ... 
doi:10.3390/s21144662 fatcat:dfln35rioncvrofuvxnmvfyyea

Complexity-adaptive universal signal estimation for compressed sensing

Junan Zhu, Dror Baron, Marco F. Duarte
2014 2014 IEEE Workshop on Statistical Signal Processing (SSP)  
We study the compressed sensing (CS) signal estimation problem where a signal is measured via a linear matrix multiplication under additive noise.  ...  For signals with independent and identically distributed (i.i.d.) entries, existing CS algorithms achieve optimal or near optimal estimation error without knowing the statistics of the signal.  ...  Final thanks to Jin Tan, Yanting Ma, and Nikhil Krishnan for commenting on our manuscript.  ... 
doi:10.1109/ssp.2014.6884657 dblp:conf/ssp/ZhuBD14 fatcat:z2v3tv52szap7cjxha76tywunm

Scalable Spectral Clustering Using Random Binning Features [article]

Lingfei Wu, Pin-Yu Chen, Ian En-Hsu Yen, Fangli Xu, Yinglong Xia and Charu Aggarwal
2019 arXiv   pre-print
Then we introduce a state-of-the-art SVD solver to effectively compute eigenvectors of this large matrix for spectral clustering.  ...  Moreover, our method exhibits linear scalability in both the number of data samples and the number of RB features.  ...  , and from at least O(KN 2 m) to O(KN Rm) for the subsequent SVD computation, where m is the number of iterations of the underlying SVD solver.  ... 
arXiv:1805.11048v3 fatcat:sjypiaimfvevhju5rs2x4vqe4y

Using multiobjective optimization to map the entropy region

László Csirmaz
2015 Computational optimization and applications  
An improved version of Benson's algorithm is presented which requires solving one scalar linear program in each iteration rather than two or three as in previous versions.  ...  Mapping the structure of the entropy region in higher dimensions is an important open problem, as even partial knowledge about this region has far reaching consequences in other areas in mathematics like  ...  We show some of the results for three different data sets.  ... 
doi:10.1007/s10589-015-9760-6 fatcat:55376tb2fvghlik2xhcnj66w5m

Using multiobjective optimization to map the entropy region of four random variables [article]

Laszlo Csirmaz
2013 arXiv   pre-print
An improved version of Benson's algorithm is described which requires solving one scalar linear program in each iteration rather than two or three as in previous versions.  ...  Presently the only available method of exploring the 15-dimensional entropy region formed by the entropies of four random variables is the one of Zhang and Yeung from 1998.  ...  We show some of the results for three different data sets.  ... 
arXiv:1310.4638v2 fatcat:uk3d6khprnaand6s6elmtfxvua
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