Data structures and network algorithms
Data structures and network algorithms
Exponentiated gradient versus gradient descent for linear predictors
Information and Computation
Introduction to Algorithms
RCV1: A New Benchmark Collection for Text Categorization Research
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Feature selection, L1 vs. L2 regularization, and rotational invariance
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Efficient Learning of Label Ranking by Soft Projections onto Polyhedra
The Journal of Machine Learning Research
Pegasos: Primal Estimated sub-GrAdient SOlver for SVM
Proceedings of the 24th international conference on Machine learning
An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression
The Journal of Machine Learning Research
Mirror descent and nonlinear projected subgradient methods for convex optimization
Operations Research Letters
Efficient Euclidean projections in linear time
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
An efficient projection for l1, ∞ regularization
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Stochastic methods for l1 regularized loss minimization
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On primal and dual sparsity of Markov networks
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Large-scale sparse logistic regression
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Primal sparse Max-margin Markov networks
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Trajectory Modeling Using Mixtures of Vector Fields
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Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Stochastic gradient descent training for L1-regularized log-linear models with cumulative penalty
ACL '09 Proceedings of the Joint Conference of the 47th Annual Meeting of the ACL and the 4th International Joint Conference on Natural Language Processing of the AFNLP: Volume 1 - Volume 1
Maximum Entropy Discrimination Markov Networks
The Journal of Machine Learning Research
Efficient Online and Batch Learning Using Forward Backward Splitting
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Online Learning for Matrix Factorization and Sparse Coding
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Proceedings of the 19th international conference on World wide web
Trajectory analysis in natural images using mixtures of vector fields
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Combined regression and ranking
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Distance metric learning from uncertain side information for automated photo tagging
ACM Transactions on Intelligent Systems and Technology (TIST)
Dual Averaging Methods for Regularized Stochastic Learning and Online Optimization
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Discovering sociolinguistic associations with structured sparsity
HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies - Volume 1
Detecting adversarial advertisements in the wild
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Conditional topical coding: an efficient topic model conditioned on rich features
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Stochastic Methods for l1-regularized Loss Minimization
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Cognitive policy learner: biasing winning or losing strategies
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
An alternating direction method for dual MAP LP relaxation
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
Cross-Lingual Adaptation Using Structural Correspondence Learning
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Extracting insights from social media with large-scale matrix approximations
IBM Journal of Research and Development
Convex and Network Flow Optimization for Structured Sparsity
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Efficient Learning with Partially Observed Attributes
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On vector and matrix median computation
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New approximation algorithms for minimum enclosing convex shapes
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Dual decomposition with many overlapping components
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Weighted consensus multi-document summarization
Information Processing and Management: an International Journal
A continuous max-flow approach to minimal partitions with label cost prior
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Segmentation of images with separating layers by fuzzy c-means and convex optimization
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Statistical Analysis and Data Mining
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Auto-grouped sparse representation for visual analysis
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IBM Journal of Research and Development
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We describe efficient algorithms for projecting a vector onto the l1-ball. We present two methods for projection. The first performs exact projection in O(n) expected time, where n is the dimension of the space. The second works on vectors k of whose elements are perturbed outside the l1-ball, projecting in O(k log(n)) time. This setting is especially useful for online learning in sparse feature spaces such as text categorization applications. We demonstrate the merits and effectiveness of our algorithms in numerous batch and online learning tasks. We show that variants of stochastic gradient projection methods augmented with our efficient projection procedures outperform interior point methods, which are considered state-of-the-art optimization techniques. We also show that in online settings gradient updates with l1 projections outperform the exponentiated gradient algorithm while obtaining models with high degrees of sparsity.