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## Section: New Results

### A probabilistic incremental proximal gradient method

Participant: Emilie Chouzenoux (Collaboration: Omer Deniz Akyildiz, Alan Turing Institute, London, UK, Victor Elvira, University of Edinburgh, Joaquin Miguez, Universidad Carlos III de Madrid, Spain)

In the paper [3], we proposed 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.