Variational Iterated Gaussian Smoothing

Implements the approximate inference algorithms from the paper Proximal Approximate Inference in State-Space Models. This code was written by Hany Abdulsamad.

varsmooth performs iterated Gaussian smoothing in nonlinear, non-Gaussian state-space models. Inference is cast as a sequence of entropic trust-region (KL-constrained) updates over a Gauss–Markov posterior, with the model expanded through generalized statistical linear regression or Fourier–Hermite moment matching. See the scripts in examples/ for demonstrations.

Installation

Install JAX for the available hardware. Then run

$ pip install -e .

for an editable install.

Smoothers

The library provides three variational smoothers (varsmooth/smoothers/):

• forward_markov — forward Gauss–Markov parameterization.
• reverse_markov — reverse Gauss–Markov parameterization.
• two_filter — combined forward/reverse (two-filter) smoother.

Each is available as a single-pass smoother, an undamped iterated smoother, and a KL-constrained iterated smoother with a temperature-based line search.

The quadratic log-potentials are built from the model with either posterior linearization (extended, cubature, unscented, gauss_hermite) or Fourier–Hermite moment matching (cubature, gauss_hermite), under varsmooth/approximation/.

Examples

Two model families are provided under examples/:

• linear_model — a linear-Gaussian system, validated against the exact RTS smoother.
• bearing_model — a nonlinear coordinated-turn (bearings-only) tracking task.

Each script selects a smoother (forward / reverse / two-filter) and an approximation, named pl_ for posterior linearization and fh_ for Fourier–Hermite. For example:

python examples/bearing_model/pl_reverse.py

Citation

If you find this code useful, please cite the paper

@article{abdulsamad2025proximal,
  title = {Proximal Approximate Inference in State-Space Models},
  author = {Hany Abdulsamad and {\'A}ngel F. Garc{\'i}a-Fern{\'a}ndez and Simo S{\"a}rkk{\"a}},
  journal = {arXiv preprint arXiv:2511.15409},
  year = {2025},
}

Credit

This project uses code snippets from sqrt-parallel-smoothers.