A randomized algorithm for closest-point queries
SIAM Journal on Computing
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
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
Convex Optimization
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
Coresets for polytope distance
Proceedings of the twenty-fifth annual symposium on Computational geometry
Maximum margin coresets for active and noise tolerant learning
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Unifying divergence minimization and statistical inference via convex duality
COLT'06 Proceedings of the 19th annual conference on Learning Theory
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
Approximating parameterized convex optimization problems
ACM Transactions on Algorithms (TALG)
Optimizing over the growing spectrahedron
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
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The problem of maximizing a concave function f(x) in the unit simplex Δ 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 Δ, such that f(x(k) ≥ f(x*) − O(1/k). Here f(x*) is the maximum value of f in Δ, and the constant factor depends on f. 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 &epsis;-coresets was shown for the minimum enclosing ball problem by means of a simple greedy algorithm. Similar greedy algorithms, which 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.