Exponentiated gradient versus gradient descent for linear predictors
Information and Computation
A decision-theoretic generalization of on-line learning and an application to boosting
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Tracking the best linear predictor
The Journal of Machine Learning Research
Tracking a small set of experts by mixing past posteriors
The Journal of Machine Learning Research
Path kernels and multiplicative updates
The Journal of Machine Learning Research
Convex Optimization
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
COLT'06 Proceedings of the 19th annual conference on Learning Theory
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Proceedings of the 24th international conference on Machine learning
Learning Permutations with Exponential Weights
The Journal of Machine Learning Research
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Artificial Intelligence Review
Kernelization of matrix updates, when and how?
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
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A number of updates for density matrices have been developed recently that are motivated by relative entropy minimization problems. The updates involve a softmin calculation based on matrix logs and matrix exponentials. We show that these updates can be kernelized. This is important because the bounds provable for these algorithms are logarithmic in the feature dimension (provided that the 2-norm of feature vectors is bounded by a constant). The main problem we focus on is the kernelization of an online PCA algorithm which belongs to this family of updates.