Estimating the largest eigenvalues by the power and Lanczos algorithms with a random start
SIAM Journal on Matrix Analysis and Applications
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Smoothing Technique and its Applications in Semidefinite Optimization
Mathematical Programming: Series A and B
Full regularization path for sparse principal component analysis
Proceedings of the 24th international conference on Machine learning
Sparse approximate solutions to semidefinite programs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
The power of convex relaxation: near-optimal matrix completion
IEEE Transactions on Information Theory
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
ACM Transactions on Algorithms (TALG)
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
The Journal of Machine Learning Research
Approximating parameterized convex optimization problems
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
| Hi-index | 0.00 |
We devise a framework for computing an approximate solution path for an important class of parameterized semidefinite problems that is guaranteed to be ε-close to the exact solution path. The problem of computing the entire regularization path for matrix factorization problems such as maximum-margin matrix factorization fits into this framework, as well as many other nuclear norm regularized convex optimization problems from machine learning. We show that the combinatorial complexity of the approximate path is independent of the size of the matrix. Furthermore, the whole solution path can be computed in near linear time in the size of the input matrix. The framework employs an approximative semidefinite program solver for a fixed parameter value. Here we use an algorithm that has recently been introduced by Hazan. We present a refined analysis of Hazan's algorithm that results in improved running time bounds for a single solution as well as for the whole solution path as a function of the approximation guarantee.