Amortised adaptive importance sampling
Abstract
Monte Carlo sampling algorithms aim to produce samples from a target distribution with a given unnormalised probability density function. The high cost of running Monte Carlo algorithms, with many simulation steps or particles needed to obtain a good empirical approximation to the target, can be reduced by introducing learnable components into the sampler -- a form of amortisation. Once these components are trained, amortised samplers can produce high-quality samples with less computation at sampling time than training-free algorithms would require. We propose an amortised sampler built upon the framework of adaptive importance sampling -- a hierarchical importance sampling procedure where the proposal is iteratively adapted. Our amortised adaptive importance sampling algorithm fits a lightweight neural network that adapts the proposal using information obtained over the course of sampling. By training our sampler over many different targets taken from the same family of distributions, we obtain a sampler that can adapt to a specific target at sampling time without a priori access to the target's parameters. We show that our procedure can efficiently sample from targets within the family the sampler was trained on, giving improvements over target-specific amortised samplers and training-free adaptive importance sampling algorithms. We also explore the potential for generalisation, where the trained sampler is used to sample from targets outwith its training family.
Related
- Repulsive normalizing flow mixtures for adaptive importance sampling: reliability analysis of complex systems
- Amortised Inference through One-Step Implicit Sampling
- Multiple Importance Sampling for Guided Speculative Inference
- Post-stratified importance sampling
- Amortized ratio-estimation importance sampling and localized simulation-based calibration for intractable likelihoods
BibTeX
@misc{carter2026amortised,
title = {{Amortised adaptive importance sampling}},
author = {Arran Carter and Víctor Elvira and Esmeralda S. Whitammer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16736},
eprint = {2610.16736},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16736},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Amortised adaptive importance sampling
AU - Arran Carter
AU - Víctor Elvira
AU - Esmeralda S. Whitammer
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16736
UR - https://arxiv.org/abs/2610.16736
AB - Monte Carlo sampling algorithms aim to produce samples from a target distribution with a given unnormalised probability density function. The high cost of running Monte Carlo algorithms, with many simulation steps or particles needed to obtain a good empirical approximation to the target, can be reduced by introducing learnable components into the sampler -- a form of amortisation. Once these components are trained, amortised samplers can produce high-quality samples with less computation at sampling time than training-free algorithms would require. We propose an amortised sampler built upon the framework of adaptive importance sampling -- a hierarchical importance sampling procedure where the proposal is iteratively adapted. Our amortised adaptive importance sampling algorithm fits a lightweight neural network that adapts the proposal using information obtained over the course of sampling. By training our sampler over many different targets taken from the same family of distributions, we obtain a sampler that can adapt to a specific target at sampling time without a priori access to the target's parameters. We show that our procedure can efficiently sample from targets within the family the sampler was trained on, giving improvements over target-specific amortised samplers and training-free adaptive importance sampling algorithms. We also explore the potential for generalisation, where the trained sampler is used to sample from targets outwith its training family.
ER -