A randomized algorithm for closest-point queries
SIAM Journal on Computing
Rounding of polytopes in the real number model of computation
Mathematics of Operations Research
Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Core Vector Machines: Fast SVM Training on Very Large Data Sets
The Journal of Machine Learning Research
Core Vector Regression for very large regression problems
ICML '05 Proceedings of the 22nd international conference on Machine learning
On approximating the smallest enclosing Bregman Balls
Proceedings of the twenty-second annual symposium on Computational geometry
Structured Prediction, Dual Extragradient and Bregman Projections
The Journal of Machine Learning Research
Computational Geometry: Theory and Applications
Maximum margin coresets for active and noise tolerant learning
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Sequential greedy approximation for certain convex optimization problems
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Generalized Core Vector Machines
IEEE Transactions on Neural Networks
Coresets for polytope distance
Proceedings of the twenty-fifth annual symposium on Computational geometry
Stochastic methods for l1 regularized loss minimization
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Sparse approximate solutions to semidefinite programs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating parameterized convex optimization problems
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A new algorithm for training SVMs using approximate minimal enclosing balls
CIARP'10 Proceedings of the 15th Iberoamerican congress conference on Progress in pattern recognition, image analysis, computer vision, and applications
Two one-pass algorithms for data stream classification using approximate MEBs
ICANNGA'11 Proceedings of the 10th international conference on Adaptive and natural computing algorithms - Volume Part II
No dimension independent core-sets for containment under homothetics
Proceedings of the twenty-seventh annual symposium on Computational geometry
INFORMS Journal on Computing
Stochastic Methods for l1-regularized Loss Minimization
The Journal of Machine Learning Research
Solving the chromatic cone clustering problem via minimum spanning sphere
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Trading Accuracy for Sparsity in Optimization Problems with Sparsity Constraints
SIAM Journal on Optimization
New approximation algorithms for minimum enclosing convex shapes
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Sublinear optimization for machine learning
Journal of the ACM (JACM)
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The problem of maximizing a concave function f(x) in a simplex S can be solved approximately by a simple greedy algorithm. For given k, the algorithm can find a point x(k) on a k-dimensional face of S, such that f(x(k)) ≥ f(x*) - O(1/k). Here f(x*) is the maximum value of f in S. This algorithm and analysis were known before, and related to problems of statistics and machine learning, such as boosting, regression, and density mixture estimation. In other work, coming from computational geometry, the existence of ε-coresets was shown for the minimum enclosing ball problem, by means of a simple greedy algorithm. Similar greedy algorithms, that are special cases of the Frank-Wolfe algorithm, were described for other enclosure problems. Here these results are tied together, stronger convergence results are reviewed, and several coreset bounds are generalized or strengthened.