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A probabilistic incremental proximal gradient method

Ömer Deniz Akyildiz 1 Emilie Chouzenoux 2, 3 Víctor Elvira 4, 5 Joaquín Míguez 1
1 UC3M - Universidad Carlos III de Madrid [Madrid]
2 GALEN-POST - Organ Modeling through Extraction, Representation and Understanding of Medical Image Content
Inria Saclay - Ile de France
3 OPIS - OPtimisation Imagerie et Santé
Inria Saclay - Ile de France, CVN - Centre de vision numérique
4 Institut TELECOM/TELECOM Lille1
5 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this paper, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the incremental proximal gradient algorithm. We explicitly model the update rules of the incremental proximal gradient method and develop a systematic approach to propagate the uncertainty of the solution estimate over iterations. The PIPG algorithm takes the form of Bayesian filtering updates for a state-space model constructed by using the cost function. Our framework makes it possible to utilize well-known exact or approximate Bayesian filters, such as Kalman or extended Kalman filters, to solve large scale regularized optimization problems.
Keywords : Proximal algorithms Probabilistic optimization Stochastic gradient Extended Kalman filtering
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Journal articles
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https://hal.archives-ouvertes.fr/hal-01946642
Contributor : Emilie Chouzenoux <>
Submitted on : Thursday, December 6, 2018 - 11:27:19 AM
Last modification on : Thursday, July 9, 2020 - 4:06:04 PM

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CNRS | INSTITUT-TELECOM | CRISTAL | INRIA | UNIV-LILLE | IMT-LILLE-DOUAI | UNIV-PARIS-SACLAY | LIGM_SIGNAL | LIGM | CVN | CENTRALESUPELEC

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Ömer Deniz Akyildiz, Emilie Chouzenoux, Víctor Elvira, Joaquín Míguez. A probabilistic incremental proximal gradient method. IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2019, 26 (8), pp.1257-1261. ⟨10.1109/LSP.2019.2926926⟩. ⟨hal-01946642⟩

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