# Analysis of Random Sequential Message Passing Algorithms for Approximate Inference

arXiv: https://arxiv.org/abs/2202.08198 · HTML: https://mlsanity.com/paper/2202.08198/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 16 Feb 2022.

## Builds on (most cited first, 10 of 10)

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classification](https://mlsanity.com/paper/2006.06098/) (2020)
- [Inference in Deep Networks in High Dimensions](https://mlsanity.com/paper/1706.06549/) (2017)
- [Approximate Survey Propagation for Statistical Inference](https://mlsanity.com/paper/1807.01296/) (2018)
- [Memory-free dynamics for the TAP equations of Ising models with arbitrary rotation invariant ensembles of random coupling matrices](https://mlsanity.com/paper/1901.08583/) (2019)
- [Generalized Approximate Survey Propagation for High-Dimensional Estimation](https://mlsanity.com/paper/1905.05313/) (2019)
- [Expectation Propagation for Approximate Inference: Free Probability Framework](https://mlsanity.com/paper/1801.05411/) (2018)
- [A Dynamical Mean-Field Theory for Learning in Restricted Boltzmann Machines](https://mlsanity.com/paper/2005.01560/) (2020)
- [Exact solution to the random sequential dynamics of a message passing algorithm](https://mlsanity.com/paper/2101.01571/) (2021)
- [Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach](https://mlsanity.com/paper/2001.04918/) (2020)

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

- [A Convergence Analysis of Approximate Message Passing with Non-Separable Functions and Applications to Multi-Class Classification](https://mlsanity.com/paper/2402.08676/) (2024)

## Abstract (arXiv)

We analyze the dynamics of a random sequential message passing algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices drawn from rotation invariant ensembles. Moreover, we consider a model mismatching setting, where the teacher model and the one used by the student may be different. By means of dynamical functional approach, we obtain exact dynamical mean-field equations characterizing the dynamics of the inference algorithm. We also derive a range of model parameters for which the sequential algorithm does not converge. The boundary of this parameter range coincides with the de Almeida Thouless (AT) stability condition of the replica symmetric ansatz for the static probabilistic model.