# A probabilistic incremental proximal gradient method

arXiv: https://arxiv.org/abs/1812.01655 · HTML: https://mlsanity.com/paper/1812.01655/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Discriminative Bayesian filtering lends momentum to the stochastic Newton method for minimizing log-convex functions](https://mlsanity.com/paper/2104.12949/) (2021)

## Abstract (arXiv)

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.