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Simulated Annealing ABC with multiple summary statistics

C Albert, S Ulzega, S Dirmeier, A Scheidegger… - arXiv preprint arXiv …, 2025 - arxiv.org
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… In Machine Learning (ML), Simulation Based Inference (… Simulation-based inference algorithms (SBI) circumvent … efficiency gain of simulation-based inference algorithms. …

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BibTeX

@article{2505.23261v1,
Author        = {Carlo Albert and Simone Ulzega and Simon Dirmeier and Andreas Scheidegger and Alberto Bassi and Antonietta Mira},
Title         = {Simulated Annealing ABC with multiple summary statistics},
Eprint        = {2505.23261v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.CO},
Abstract      = {Bayesian inference for stochastic models is often challenging because
evaluating the likelihood function typically requires integrating over a large
number of latent variables. However, if only few parameters need to be
inferred, it can be more efficient to perform the inference based on a
comparison of the observations with (a large number of) model simulations, in
terms of only few summary statistics. In Machine Learning (ML), Simulation
Based Inference (SBI) using neural density estimation is often considered
superior to the traditional sampling-based approach known as Approximate
Bayesian Computation (ABC). Here, we present a new set of ABC algorithms based
on Simulated Annealing and demonstrate that they are competitive with ML
approaches, whilst requiring much less hyper-parameter tuning. For the design
of these sampling algorithms we draw intuition from non-equilibrium
thermodynamics, where we associate each summary statistic with a state variable
(energy) quantifying the distance to the observed value as well as a
temperature that controls the degree to which the associated statistic
contributes to the posterior. We derive an optimal annealing schedule on a
Riemannian manifold of state variables based on a minimal entropy production
principle. Our new algorithms generalize the established Simulated Annealing
based ABC to multiple state variables and temperatures. In situations where the
information-content is unevenly distributed among the summary statistics, this
can greatly improve performance of the algorithm. Our method also allows
monitoring the convergence of individual statistics, which is a great
diagnostic tool in out-of-sample situations. We validate our approach on
standard benchmark tasks from the SBI literature and a hard inference problem
from solar physics and demonstrate that it is highly competitive with the
state-of-the-art.},
Year          = {2025},
Month         = {May},
Url           = {http://arxiv.org/abs/2505.23261v1},
File          = {2505.23261v1.pdf}
}

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