Multi-modal Laplace-based sampling
Abstract
We study the multi-modal Laplace approximation, given by a weighted Gaussian mixture centred at the local minima of the negative log-density, for sampling from probability measures that concentrate around finitely many modes as an inverse-temperature parameter n grows. Such distributions occur in Bayesian inference in the small noise or large data regime. We derive explicit, non-asymptotic bounds on the Hellinger distance between the multi-modal Laplace approximation and the concentrating posterior. The bound decays like n−1/2 with n and the constants depend only polynomially on the dimension d. Moreover, we analyse the Laplace mixture as a proposal distribution for self-normalised importance sampling and independent Metropolis--Hastings (IMH) targeting concentration multimodal distributions. We derive asymptotic results, as n→∞, on the effective sample size in case of importance sampling as well as on the average acceptance probability, lag-one autocorrelation, and spectral gap in case of IMH. Numerical experiments illustrate and verify our theoretical findings.
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BibTeX
@misc{egea2026multimodal,
title = {{Multi-modal Laplace-based sampling}},
author = {Maxime Egéa and Hanyue Gu and Daniel Rudolf and Björn Sprungk},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03773},
eprint = {2611.03773},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03773},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multi-modal Laplace-based sampling
AU - Maxime Egéa
AU - Hanyue Gu
AU - Daniel Rudolf
AU - Björn Sprungk
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03773
UR - https://arxiv.org/abs/2611.03773
AB - We study the multi-modal Laplace approximation, given by a weighted Gaussian mixture centred at the local minima of the negative log-density, for sampling from probability measures that concentrate around finitely many modes as an inverse-temperature parameter n grows. Such distributions occur in Bayesian inference in the small noise or large data regime. We derive explicit, non-asymptotic bounds on the Hellinger distance between the multi-modal Laplace approximation and the concentrating posterior. The bound decays like n^−1/2 with n and the constants depend only polynomially on the dimension d. Moreover, we analyse the Laplace mixture as a proposal distribution for self-normalised importance sampling and independent Metropolis--Hastings (IMH) targeting concentration multimodal distributions. We derive asymptotic results, as n→∞, on the effective sample size in case of importance sampling as well as on the average acceptance probability, lag-one autocorrelation, and spectral gap in case of IMH. Numerical experiments illustrate and verify our theoretical findings.
ER -