sabc

Simulated Annealing ABC in MLX

sabc performs likelihood-free Bayesian inference (Approximate Bayesian Computation) via Simulated Annealing. The annealing loop — empirical-CDF distance transform, importance resampling, epsilon schedule, and a Differential-Evolution MCMC kernel — runs in a compiled nanobind extension (sabc._core), while models, priors, and the entry point live in Python and exchange mlx.core.arrays with the C++ core zero-copy via DLPack.

Quickstart

All you provide is a prior, the observed data, and a distance function f_dist(theta, observed). The distance function is yours to write — it folds simulation, summary statistics, and the metric into one place — and it returns either one distance per particle (scalar) or one per summary statistic (vector). Here we infer the location of a 2-D model observed at [1, -1]:

import mlx.core as mx

import sabc
from sabc import distributions as dist

observed = mx.array([1.0, -1.0])

prior = dist.JointDistributionNamed(
    dict(theta=dist.Normal(mx.zeros(2), mx.ones(2) * 3.0))
)


def f_dist(theta, observed):
    # theta: (n_particles, n_para). Simulate, then return the distance(s).
    y = theta + mx.random.normal(theta.shape) * 0.1
    return mx.abs(y - observed)              # per-dimension (vector) distance


posterior = sabc.run(
    f_dist,
    prior=prior,
    observed=observed,
    n_particles=2000,
    n_simulation=200_000,
    schedule=sabc.SingleEps(v=1.0),
    key=mx.random.key(0),
)

print(posterior.samples.mean(axis=0))      # ~ [1, -1]

sabc.run returns a Posterior with samples, u, rho, and the epsilon_history / u_history traces.

Scalar vs vector distances, single vs multiple epsilon

The shape of what f_dist returns chooses the inference flavour, independently of the epsilon schedule:

• return (n_particles,) / (n_particles, 1) for a single scalar distance,
• return (n_particles, n_stats) to keep one distance per summary statistic.

A per-statistic distance pairs naturally with MultiEps, which anneals one temperature per statistic (SingleEps uses one shared temperature):

def f_dist(theta, observed):
    y = simulate(theta)
    return mx.abs(summary(y) - observed)    # (n_particles, n_stats)

posterior = sabc.run(
    f_dist, prior=prior, observed=observed,
    schedule=sabc.MultiEps(v=1.0),          # one epsilon per statistic
)

Priors

Priors are built from MLX-native, TFP-style distributions:

prior = dist.JointDistributionNamed(dict(
    a=dist.Normal(mx.zeros(1), mx.ones(1)),
    b=lambda a: dist.Normal(a, mx.ones(1)),   # p(b | a)
))

Examples

Self-contained examples are in examples.

Installation

sabc targets Apple Silicon (Metal); Linux support is experimental. It requires Python ≥ 3.11. Install the released package from PyPI:

pip install sabc

For a development checkout, use uv:

git clone https://github.com/dirmeier/sabc && cd sabc
uv sync --all-extras

Development

The project uses uv, scikit-build-core (CMake/C++23), ruff for Python, and clang-format + cpplint for C++. The Makefile wraps the common tasks:

make check    # cpp checks
make tests    # run the tests
make format   # autoformat
make lints    # lint

Install the git hooks once (the commit-msg type is needed for gitlint):

uv run pre-commit install --hook-type pre-commit --hook-type commit-msg

The hooks then run automatically on changed files at commit time. To run every hook against the whole repository (useful after adding a hook or before a PR):

uv run pre-commit run --all-files

Linux build (Docker)

The CI builds the C++/MLX extension under gcc on Linux. Apple clang accepts some MLX overloads that gcc rejects, so a dev container is provided to reproduce and verify the Linux build locally without GitHub Actions:

docker build -t sabc-linux -f .devcontainer/Dockerfile .
docker run --rm -v "$PWD":/work -w /work sabc-linux \
  bash -lc "uv sync --all-extras && make tests"

Citing SABC

If you find this package relevant to your research, please consider citing:

@article{albert2025simulated,
  title={Simulated Annealing ABC with multiple summary statistics},
  author={Albert, Carlo and Ulzega, Simone and Dirmeier, Simon and Scheidegger, Andreas and Bassi, Alberto and Mira, Antonietta},
  journal={arXiv preprint arXiv:2505.23261},
  year={2025}
}