The Incremental Proximal Method: A Probabilistic Perspective

Omer Deniz Akyildiz*, Victor Elvira, Joaquin Miguez

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be realized with, Bayes updates. We give the explicit form of the updates for the linear regression problem and show that there is a one-to-one correspondence between the proximal operator of the least-squares regression and the Bayes update when the prior and the likelihood are Gaussian. We then carry out this observation to a general sequential setting: We consider the incremental proximal method, which is an algorithm for large-scale optimization, and show that, for a linear-quadratic cost function, it can naturally be realized by the Kalman filter. We then discuss the implications of this idea for nonlinear optimization problems where proximal operators are in general not realizable. In such settings, we argue that the extended Kalman filter can provide a systematic way for the derivation of practical procedures.

Original languageEnglish
Title of host publication2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4279-4283
Number of pages5
Volume2018-April
ISBN (Print)9781538646588
DOIs
Publication statusPublished - 10 Sep 2018
Event2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Calgary, Canada
Duration: 15 Apr 201820 Apr 2018

Conference

Conference2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
Country/TerritoryCanada
CityCalgary
Period15/04/1820/04/18

Keywords

  • Incremental proximal methods
  • Kalman filtering
  • Stochastic optimization

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