- A framework based on symbolic regression coupled with eXtended Physics-Informed Neural Networks for gray-box learning of equations of motion from data
2023/07/25 by Elham Kiyani, Khemraj Shukla, George Em Karniadakis +1 · 30 citations
Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Computer science #Domain (mathematical analysis) #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Mathematical analysis #Mathematics #Matrix norm #Model Reduction and Neural Networks #Noise (video) #Nonlinear system #Norm (philosophy) #Physics #Symbolic regression #Test data
- An ℓp theory of PCA and spectral clustering
2022/08/01 by Emmanuel Abbe, Emmanuel Abbé, Jianqing Fan +1 · 32 citations
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Blind Source Separation Techniques #Cluster analysis #Computer science #Eigenvalues and eigenvectors #Gaussian #Heteroscedasticity #Mathematics #Matrix norm #Pattern recognition (psychology) #Principal component analysis #Random Matrices and Applications #Sparse PCA #Sparse and Compressive Sensing Techniques #Spectral clustering #Statistics
- Most Tensor Problems Are NP-Hard
2013/11/01 by Christopher J. Hillar, Lek-Heng Lim, Lek‐Heng Lim · 1,150 citations
Computer Science · Mathematics · #Algebra over a field #Bilinear form #Bilinear interpolation #Cartesian tensor #Combinatorics #Eigenvalues and eigenvectors #Exact solutions in general relativity #Jordan algebra #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Matrix norm #Multilinear algebra #Multilinear map #Norm (philosophy) #Numerical Methods and Algorithms #Physics #Pure mathematics #Quantum mechanics #Rank (graph theory) #Singular value #Symmetric tensor #Tensor (intrinsic definition) #Tensor algebra #Tensor decomposition and applications #Tensor density #Tensor field
- A Constrainedℓ1Minimization Approach to Sparse Precision Matrix Estimation
2011/03/29 by Tommaso Cai, Weidong Liu, Xi Luo · 1,059 citations
Engineering · Mathematics · #Algorithm #Applied mathematics #Computer science #Estimation of covariance matrices #Estimator #Mathematical optimization #Mathematics #Matrix norm #Random Matrices and Applications #Rate of convergence #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics
- Nuclear norm penalization and optimal rates for noisy low rank matrix\n completion
2010/11/29 by Vladimir Koltchinskii, Koltchinskii, Vladimir, Alexandre B. Tsybakov +3 · 649 citations
Engineering · Mathematics · #Advanced SAR Imaging Techniques #Applied mathematics #Combinatorics #Eigenvalues and eigenvectors #Estimator #Logarithm #Mathematical analysis #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix completion #Matrix norm #Minimax #Numerical methods in inverse problems #Rank (graph theory) #Rate of convergence #Sparse and Compressive Sensing Techniques #Statistics #Upper and lower bounds #math.ST #msc:60B20 #msc:60G15 #msc:62H12 #msc:62J99 #stat.ML #stat.TH
- Optimal rates of convergence for covariance matrix estimation
2010/07/12 by T. Tony Cai, Cun-Hui Zhang, Harrison H. Zhou · 315 citations
Computer Science · Mathematics · #Covariance #Covariance matrix #Covariance operator #Direction-of-Arrival Estimation Techniques #Distributed Sensor Networks and Detection Algorithms #Estimation of covariance matrices #Estimator #Matrix norm #Minimax #Random Matrices and Applications #Rate of convergence #math.ST #stat.TH
- Collaborative Filtering in a Non-Uniform World: Learning with the Weighted Trace Norm
2010/02/14 by Ruslan Salakhutdinov, Salakhutdinov, Ruslan, Nathan Srebro +1 · 68 citations
Chemistry · Computer Science · Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #Algorithm #Applied mathematics #Artificial intelligence #Chemistry #Computer science #Epistemology #FOS: Computer and information sciences #Indoor and Outdoor Localization Technologies #Machine Learning (cs.LG) #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix norm #Norm (philosophy) #Physics #Regularization (linguistics) #Sparse and Compressive Sensing Techniques #TRACE (psycholinguistics) #cs.LG
- Tight oracle bounds for low-rank matrix recovery from a minimal number of random measurements
2010/01/02 by Emmanuel J. Candès, Emmanuel J. Candes, Candes, Emmanuel J. +2 · 143 citations
Computer Science · Engineering · Mathematics · #Advanced SAR Imaging Techniques #Algorithm #Applied mathematics #Combinatorics #Compressed sensing #Computer science #Constant (computer programming) #Discrete mathematics #Eigenvalues and eigenvectors #Estimator #FOS: Computer and information sciences #Gaussian #Information Theory (cs.IT) #Low-rank approximation #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix completion #Matrix norm #Microwave Imaging and Scattering Analysis #Minimax #Oracle #Physics #Pure mathematics #Rank (graph theory) #Restricted isometry property #Sparse and Compressive Sensing Techniques #Statistics #cs.IT #math.IT
- Operator norm consistent estimation of large-dimensional sparse covariance matrices
2008/12/01 by Noureddine El Karoui · 246 citations
Computer Science · Mathematics · #Consistency (knowledge bases) #Covariance #Covariance matrix #Eigenvalues and eigenvectors #Estimation of covariance matrices #Estimator #Law of total covariance #Matrix Theory and Algorithms #Matrix norm #Population #Random Matrices and Applications #Scatter matrix #Stochastic Gradient Optimization Techniques #math.ST #msc:62H12 #stat.TH
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
2007/06/28 by Benjamin Recht, Maryam Fazel, Pablo A. Parrilo · 3,628 citations
Computer Science · Engineering · Mathematics · #Affine transformation #Algorithm #Blind Source Separation Techniques #Combinatorics #Compressed sensing #Indoor and Outdoor Localization Technologies #Linear map #Mathematical optimization #Mathematics #Matrix norm #Minification #Pure mathematics #Rank (graph theory) #Restricted isometry property #Sparse and Compressive Sensing Techniques #math.OC #math.ST #msc:15A52 #msc:90C25 #msc:90C59 #stat.TH