Learned proposals in trans-dimensional inference are optimal at equilibrium, not during assembly

Argyro Sasli; Nikolaos Karnesis; Minas Karamanis; Michael L. Katz; Dimitrios Kourtesis; Michael W. Coughlin; Vuk Mandic; Nikolaos Stergioulas

arXiv · 2608.12392

Learned proposals in trans-dimensional inference are optimal at equilibrium, not during assembly

Argyro Sasli·Nikolaos Karnesis·Minas Karamanis·Michael L. Katz·Dimitrios Kourtesis·Michael W. Coughlin·Vuk Mandic·Nikolaos Stergioulas

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Abstract

Inferring the dimension of a model - the number of components needed to explain data - jointly with the parameters is a pervasive problem, from counting sources in an image to mixture modeling, and reversible-jump Markov chain Monte Carlo solves it exactly but mixes slowly. Learned proposals are well established at fixed dimension, but whether they can accelerate the dimension-changing moves themselves has remained largely untested. We show that the answer has a structural origin: the optimal proposal for the dimension-changing birth move is a different object in different phases of the run. While the fit is being assembled it must match the current residual - a state-dependent quantity no state-independent network can represent - but at equilibrium it degenerates to the posterior's single-component marginal, which is exactly the distribution an adaptive normalizing flow learns from the sampler's own history. A learned state-independent birth proposal is therefore useless in one phase and optimal in the other. Controlled experiments confirm the attribution: applied with an exact Metropolis--Hastings correction that leaves the target invariant for any network, the learned births leave acceptance rates unchanged yet accelerate model-order mixing - in a ten-seed benchmark they meet a pre-specified stopping rule in six of ten runs, typically several times sooner, where a strong hand-tuned baseline meets it in one (one-sided p=0.03) - and an isolation experiment shows the same flow deployed within-model buys nothing. Making no domain-specific assumptions, the same sampler counts sources in a noisy image and reconstructs signals across scientific domains, including gravitational waves from ground- and space-based detectors and a scalp EEG recording. We release the method as HyperWave, an open-source package.

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BibTeX RIS

Argyro Sasli, Nikolaos Karnesis, Minas Karamanis, Michael L. Katz, Dimitrios Kourtesis, Michael W. Coughlin, Vuk Mandic, Nikolaos Stergioulas. 2026-08-04. Learned proposals in trans-dimensional inference are optimal at equilibrium, not during assembly. https://arxiv.org/abs/2608.12392

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