Combinatorial preconditioners for proximal algorithms on graphs
Möllenhoff T, Ye Z, Wu T, Cremers D (2018)
Publication Type: Conference contribution
Publication year: 2018
Publisher: PMLR
Pages Range: 38-47
Conference Proceedings Title: International Conference on Artificial Intelligence and Statistics, AISTATS 2018
Event location: Playa Blanca, Lanzarote, Canary Islands, ESP
Abstract
We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We prove that certain decompositions lead to a theoretically optimal condition number. We also show how ideal decompositions can be realized using matroid partitioning and propose efficient greedy variants thereof for large-scale problems. Coupled with specialized solvers for the resulting scaled proximal subproblems, the preconditioned algorithm achieves competitive performance in machine learning and vision applications.
Involved external institutions
Germany (DE)How to cite
APA:
Möllenhoff, T., Ye, Z., Wu, T., & Cremers, D. (2018). Combinatorial preconditioners for proximal algorithms on graphs. In Amos J. Storkey, Fernando Perez-Cruz (Eds.), International Conference on Artificial Intelligence and Statistics, AISTATS 2018 (pp. 38-47). Playa Blanca, Lanzarote, Canary Islands, ESP: PMLR.
MLA:
Möllenhoff, Thomas, et al. "Combinatorial preconditioners for proximal algorithms on graphs." Proceedings of the 21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018, Playa Blanca, Lanzarote, Canary Islands, ESP Ed. Amos J. Storkey, Fernando Perez-Cruz, PMLR, 2018. 38-47.
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