From on-line to batch learning
COLT '89 Proceedings of the second annual workshop on Computational learning theory
Matrix computations (3rd ed.)
Exponentiated gradient versus gradient descent for linear predictors
Information and Computation
Machine Learning - Special issue on context sensitivity and concept drift
Linear hinge loss and average margin
Proceedings of the 1998 conference on Advances in neural information processing systems II
Quantum computation and quantum information
Quantum computation and quantum information
Tracking the best linear predictor
The Journal of Machine Learning Research
Matrix Exponentiated Gradient Updates for On-line Learning and Bregman Projection
The Journal of Machine Learning Research
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Online kernel PCA with entropic matrix updates
Proceedings of the 24th international conference on Machine learning
When is there a free matrix lunch?
COLT'07 Proceedings of the 20th annual conference on Learning theory
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Linear Algorithms for Online Multitask Classification
The Journal of Machine Learning Research
Regression on Fixed-Rank Positive Semidefinite Matrices: A Riemannian Approach
The Journal of Machine Learning Research
Kernelization of matrix updates, when and how?
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
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We generalize the Winnow algorithm for learning disjunctions to learning subspaces of low rank. Subspaces are represented by symmetric projection matrices. The online algorithm maintains its uncertainty about the hidden low rank projection matrix as a symmetric positive definite matrix. This matrix is updated using a version of the Matrix Exponentiated Gradient algorithm that is based on matrix exponentials and matrix logarithms. As in the case of the Winnow algorithm, the bounds are logarithmic in the dimension n of the problem, but linear in the rank r of the hidden subspace. We show that the algorithm can be adapted to handle arbitrary matrices of any dimension via a reduction.