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SPSD Matrix Approximation vis Column Selection: Theories, Algorithms, and Extensions [article]

Shusen Wang, Luo Luo, Zhihua Zhang
2016 arXiv   pre-print
Second, we develop a simple column selection algorithm with a provable error bound.  ...  In this paper we conduct in-depth studies of an SPSD matrix approximation model and establish strong relative-error bounds.  ...  Luo and Zhang have been supported by the National Natural Science Foundation of China (No. 61572017), Natural Science Foundation of Shanghai City (No. 15ZR1424200), and Microsoft Research Asia Collaborative  ... 
arXiv:1406.5675v6 fatcat:eud5zudl7jeedgyvdj6q6ic34i

Anisotropic Scale Selection, Robust Gaussian Fitting, and Pulmonary Nodule Segmentation in Chest CT Scans [chapter]

Kazunori Okada
2011 Multi Modality State-of-the-Art Medical Image Segmentation and Registration Methodologies  
The theory combines two distinct concepts for generic data analysis: automatic scale selection and robust Gaussian model fitting.  ...  This chapter presents the theory and design principles used to derive semi-automatic algorithms for pulmonary nodule segmentation toward realizing a reliable and reproducible clinical application for nodule  ...  ANISOTROPIC SCALE SELECTION This section presents the theory for anisotropic scale selection.  ... 
doi:10.1007/978-1-4419-8195-0_3 fatcat:sva6y55wvnbmlaassfpnnfu24i

Improved Fixed-Rank Nyström Approximation via QR Decomposition: Practical and Theoretical Aspects [article]

Farhad Pourkamali-Anaraki, Stephen Becker
2017 arXiv   pre-print
To address these issues, we present an efficient method for generating improved fixed-rank Nystr\"om approximations.  ...  In practice, to ensure high quality approximations, the number of landmark points is chosen to be greater than the target rank.  ...  This column selection process can be viewed as forming a sampling matrix P ∈ R n×m that has exactly one nonzero entry in each column, where its location corresponds to the index of the selected landmark  ... 
arXiv:1708.03218v1 fatcat:h6wasfclt5egzll354epufjx7q

Convergence of Sparse Variational Inference in Gaussian Processes Regression [article]

David R. Burt and Carl Edward Rasmussen and Mark van der Wilk
2020 arXiv   pre-print
In this work, we investigate upper and lower bounds on how M needs to grow with N to ensure high quality approximations.  ...  We show that we can make the KL-divergence between the approximate model and the exact posterior arbitrarily small for a Gaussian-noise regression model with M≪ N.  ...  Acknowledgments We would particularly like to thank Guillaume Gautier for pointing out an error in the exact k-DPP sampling algorithm cited in an earlier version of this work, and for guiding us through  ... 
arXiv:2008.00323v1 fatcat:pzr6cpuclzae7bpdol35ileavu

Probability-Distribution-Based Node Pruning for Sphere Decoding

Tao Cui, Shuangshuang Han, Chintha Tellambura
2013 IEEE Transactions on Vehicular Technology  
His research interests include the interactions between networking theory, communication theory, and information theory.  ...  Simulation results show that threshold pruning saves complexity compared with popular sphere decoder (SD) algorithms, such as the K-best SD, the fixed-complexity SD (FSD), and the probabilistic tree pruning  ...  The extension of our proposed algorithms to the Fincke-Phost SD [2] is straightforward.  ... 
doi:10.1109/tvt.2012.2233226 fatcat:oizf4ggrlvg65kvt64yk6l5ox4

Algorithms that satisfy a stopping criterion, probably [article]

Uri Ascher, Farbod Roosta-Khorasani
2014 arXiv   pre-print
We describe an algorithm that becomes more efficient in a controlled way as the uncertainty in the tolerance increases, and demonstrate this in the context of some particular applications of inverse problems  ...  This is a useful setting for comparing algorithm performance, among other purposes.  ...  Acknowledgments The authors thank Eldad Haber and Arieh Iserles for several fruitful discussions. References  ... 
arXiv:1408.5946v2 fatcat:6vog5at5qbbftlocnuhpygga7e

Assessing Stochastic Algorithms for Large Scale Nonlinear Least Squares Problems Using Extremal Probabilities of Linear Combinations of Gamma Random Variables

Farbod Roosta-Khorasani, Gábor J. Székely, Uri M. Ascher
2015 SIAM/ASA Journal on Uncertainty Quantification  
(SPSD) matrices.  ...  Such stochastic steps involve approximating the NLS objective function using Monte-Carlo methods, and this is equivalent to the estimation of the trace of corresponding symmetric positive semi-definite  ...  The graph shows the fitting sample size growth for variants (ii) and (vi) of Algorithm 1, as well as their counterparts, namely, variants (vi) and (viii).  ... 
doi:10.1137/14096311x fatcat:tdux3nha6jezdcsknap4evkvmi

Sketchy Empirical Natural Gradient Methods for Deep Learning [article]

Minghan Yang, Dong Xu, Zaiwen Wen, Mengyun Chen, Pengxiang Xu
2021 arXiv   pre-print
The empirical Fisher information matrix is usually low-rank since the sampling is only practical on a small amount of data at each iteration.  ...  Extensive experiments on convolutional neural networks show the competitiveness of SENG compared with the state-of-the-art methods.  ...  Wang, S., Luo, L., and Zhang, Z. Spsd matrix approximation vis column selection: Theories, algorithms, and extensions. J. Mach. Learn. Res., 17(1):1697-1745, January 2016. ISSN 1532-4435.  ... 
arXiv:2006.05924v3 fatcat:qvmrz2lyffcajm2w5qnovtyxye

Communication-Efficient Distributed SVD via Local Power Iterations [article]

Xiang Li, Shusen Wang, Kun Chen, Zhihua Zhang
2021 arXiv   pre-print
We develop an algorithm that we call for improving communication efficiency.  ...  As a practical surrogate of OPT, sign-fixing, which uses a diagonal matrix with ± 1 entries as weights, has better computation complexity and stability in experiments.  ...  SPSD matrix approximation vis column selection: Theories, algorithms, and extensions. Journal of Machine Learning Research, 17 284-309, 2016a. 8, 22, 23 236-249. ACM, 2016. 8 Candès, E.  ... 
arXiv:2002.08014v4 fatcat:p77p3kdoa5aezjipdyrmykemfm

TOA Estimation for Positioning With DVB-T Signals in Outdoor Static Tests

Liang Chen, Olivier Julien, Paul Thevenon, Damien Serant, Axel Garcia Pena, Heidi Kuusniemi
2015 IEEE transactions on broadcasting  
then algorithms of the coarse symbol synchronization, the pilot detection, the first path acquisition and the delay tracking are sequentially performed to obtain the TOA estimation.  ...  Therefore, the DTV signal does not experience significantly the Doppler effects and the impairment caused by the delay of ionosphere propagation, which will lead to easier signal acquisition and the possibility  ...  ) With the new column c sq selected, the matrix R q and C q are updated as R q = [ C s,q−1 c sq ] * [ C s,q−1 c sq ] z q = [ C s,q−1 c sq ] * d (18) The iterative search process stops when no more path  ... 
doi:10.1109/tbc.2015.2465155 fatcat:4voqe2xnxbcp7dq5hsxkxinmom

Convergence of Sparse Variational Inference in Gaussian Processes Regression

David Burt, Carl Rasmussen, Mark Van Der Wilk, Apollo-University Of Cambridge Repository
2020
In this work, we investigate upper and lower bounds on how M needs to grow with N to ensure high quality approximations.  ...  We show that we can make the KL-divergence between the approximate model and the exact posterior arbitrarily small for a Gaussian-noise regression model with M<  ...  Acknowledgments We would particularly like to thank Guillaume Gautier for pointing out an error in the exact k-DPP sampling algorithm cited in an earlier version of this work, and for guiding us through  ... 
doi:10.17863/cam.55909 fatcat:yk2xz4y57nbpfcv42p6jfbiqla

Algorithmic Results for Clustering and Refined Physarum Analysis [article]

Pavel Kolev, Universität Des Saarlandes, Universität Des Saarlandes
2018
In addition, we give novel algorithms for important variants of 0 -low rank approximation.  ...  In the first part of this thesis, we study the Binary 0 -Rank-k problem which given a binary matrix A and a positive integer k, seeks to find a rank-k binary matrix B minimizing the number of non-zero  ...  Woodruff for inspiring this study and for fruitful collaboration, and Uriel Feige for helpful discussions and for pointing me to the work of Alon and Sudakov [AS99] .  ... 
doi:10.22028/d291-27551 fatcat:itwp3hnlhncm5avwyn3gucq4zi

Model updating in structural dynamics: advanced parametrization, optimal regularization, and symmetry considerations

Daniel Thomas Bartilson
2018
In structural engineering, finite element (FE) models are extensively used to predict responses and estimate risk for built structures.  ...  Numerical models are pervasive tools in science and engineering for simulation, design, and assessment of physical systems.  ...  Acknowledgments The authors gratefully acknowledge Columbia University's Graduate School of Arts and Sciences in support of the first author through the Guggenheim Fellowship and Presidential Fellowship  ... 
doi:10.7916/d8dn5p2c fatcat:afiekauyafh5zni6ccm5hv7z4q

Numerical aspects of flow stabilization by Riccati feedback [article]

Heiko K. Weichelt, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Peter Benner
2018
Many people have contributed to my work and to my life.  ...  Strongly connected to this is the problem of a proper approximation theory for the computed feedback matrix K.  ...  [26, Rem. 4] ) If the current iterate X (k) is spsd, if the solution X (k+1) of (6.7) is spsd, and if ξ k ∈ (0, 1], then X (k+1) defined by (6.11) is also spsd.  ... 
doi:10.25673/4493 fatcat:whkogagkmzcb3cl6oysejrcvzq

Learning and Reasoning with Fast Semidefinite Programming and Mixing Methods

Po-wei Wang
2022
We also show that the Mixing method can accurately estimate the mode and partition function of the pairwise Markov Random Fields, and scales to millions of variables.  ...  In this thesis, we aim to break the barrier and bring SDP's power back to large-scale machine learning problems.  ...  And S = C + diag(y) 0 follows from the dual feasibility. By the characterization of SPSD matrix, all submatrix of S 0 are SPSD. Thus, y i ≥ 0.  ... 
doi:10.1184/r1/19630071 fatcat:ohzdu5xr6rak7bnioaf4rdgh6m
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