A least squares formulation for a class of generalized eigenvalue problems in machine learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Fast communication: Mixed linear system estimation and identification
Signal Processing
Weight-decay regularization in reproducing Kernel Hilbert spaces by variable-basis schemes
WSEAS Transactions on Mathematics
A Fast Hybrid Algorithm for Large-Scale l1-Regularized Logistic Regression
The Journal of Machine Learning Research
A subband adaptive iterative shrinkage/thresholding algorithm
IEEE Transactions on Signal Processing
Solving low-rank matrix completion problems efficiently
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Bayesian compressive sensing via belief propagation
IEEE Transactions on Signal Processing
Beyond Nyquist: efficient sampling of sparse bandlimited signals
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
Projected Landweber iteration for matrix completion
Journal of Computational and Applied Mathematics
IEEE Transactions on Audio, Speech, and Language Processing - Special issue on processing reverberant speech: methodologies and applications
Solving structured sparsity regularization with proximal methods
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part II
Fast optimization for mixture prior models
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Optimum subspace learning and error correction for tensors
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Computational Statistics & Data Analysis
A non-adapted sparse approximation of PDEs with stochastic inputs
Journal of Computational Physics
The Journal of Machine Learning Research
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
SIAM Journal on Scientific Computing
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
Sparse Signal Reconstruction via Iterative Support Detection
SIAM Journal on Imaging Sciences
Robust principal component analysis?
Journal of the ACM (JACM)
The minimum-rank gram matrix completion via modified fixed point continuation method
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Composite splitting algorithms for convex optimization
Computer Vision and Image Understanding
Analysis and Generalizations of the Linearized Bregman Method
SIAM Journal on Imaging Sciences
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
Gradient-Based Methods for Sparse Recovery
SIAM Journal on Imaging Sciences
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
A First-Order Smoothed Penalty Method for Compressed Sensing
SIAM Journal on Optimization
SIAM Journal on Imaging Sciences
Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Codes
SIAM Journal on Imaging Sciences
Mining discriminative components with low-rank and sparsity constraints for face recognition
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Accelerated Block-coordinate Relaxation for Regularized Optimization
SIAM Journal on Optimization
Error Forgetting of Bregman Iteration
Journal of Scientific Computing
Accelerated Linearized Bregman Method
Journal of Scientific Computing
Computational Optimization and Applications
Advances in Computational Mathematics
Shadow-Free TILT for facade rectification
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part IV
Recovering low-rank matrices from corrupted observations via the linear conjugate gradient algorithm
Journal of Computational and Applied Mathematics
Large-scale multilabel propagation based on efficient sparse graph construction
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)
Sparse signal reconstruction using decomposition algorithm
Knowledge-Based Systems
Nonparametric sparsity and regularization
The Journal of Machine Learning Research
Transform invariant text extraction
The Visual Computer: International Journal of Computer Graphics
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We present a framework for solving the large-scale $\ell_1$-regularized convex minimization problem:\[ \min\|x\|_1+\mu f(x). \] Our approach is based on two powerful algorithmic ideas: operator-splitting and continuation. Operator-splitting results in a fixed-point algorithm for any given scalar $\mu$; continuation refers to approximately following the path traced by the optimal value of $x$ as $\mu$ increases. In this paper, we study the structure of optimal solution sets, prove finite convergence for important quantities, and establish $q$-linear convergence rates for the fixed-point algorithm applied to problems with $f(x)$ convex, but not necessarily strictly convex. The continuation framework, motivated by our convergence results, is demonstrated to facilitate the construction of practical algorithms.