# Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach

arXiv: https://arxiv.org/abs/2001.04918 · HTML: https://mlsanity.com/paper/2001.04918/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2020.

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

- [Analysis of Random Sequential Message Passing Algorithms for Approximate Inference](https://mlsanity.com/paper/2202.08198/) (2022)

## Abstract (arXiv)

We analyze the dynamics of an 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. For the case of perfect data-model matching, the knowledge of static order parameters derived from the replica method allows us to obtain efficient algorithmic updates in terms of matrix-vector multiplications with a fixed matrix. Using the dynamical functional approach, we obtain an exact effective stochastic process in the thermodynamic limit for a single node. From this, we obtain closed-form expressions for the rate of the convergence. Analytical results are excellent agreement with simulations of single instances of large models.