# Deep Importance Sampling based on Regression for Model Inversion and Emulation

arXiv: https://arxiv.org/abs/2010.10346 · HTML: https://mlsanity.com/paper/2010.10346/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [A survey of Monte Carlo methods for noisy and costly densities with application to reinforcement learning and ABC](https://mlsanity.com/paper/2108.00490/) (2021)
- [Bayesian neural networks via MCMC: a Python-based tutorial](https://mlsanity.com/paper/2304.02595/) (2023)
- [On the safe use of prior densities for Bayesian model selection](https://mlsanity.com/paper/2206.05210/) (2022)
- [MCMC-driven importance samplers](https://mlsanity.com/paper/2105.02579/) (2021)
- [Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals](https://mlsanity.com/paper/2501.01148/) (2025)
- [Data-driven informative priors for Bayesian inference with quasi-periodic data](https://mlsanity.com/paper/2511.22296/) (2025)
- [A note on the area under the likelihood and the fake evidence for model selection](https://mlsanity.com/paper/2602.22965/) (2026)
- [An automatic counting algorithm for the quantification and uncertainty analysis of the number of microglial cells trainable in small and heterogeneous datasets](https://mlsanity.com/paper/2602.22974/) (2026)

## Abstract (arXiv)

Understanding systems by forward and inverse modeling is a recurrent topic of research in many domains of science and engineering. In this context, Monte Carlo methods have been widely used as powerful tools for numerical inference and optimization. They require the choice of a suitable proposal density that is crucial for their performance. For this reason, several adaptive importance sampling (AIS) schemes have been proposed in the literature. We here present an AIS framework called Regression-based Adaptive Deep Importance Sampling (RADIS). In RADIS, the key idea is the adaptive construction via regression of a non-parametric proposal density (i.e., an emulator), which mimics the posterior distribution and hence minimizes the mismatch between proposal and target densities. RADIS is based on a deep architecture of two (or more) nested IS schemes, in order to draw samples from the constructed emulator. The algorithm is highly efficient since employs the posterior approximation as proposal density, which can be improved adding more support points. As a consequence, RADIS asymptotically converges to an exact sampler under mild conditions. Additionally, the emulator produced by RADIS can be in turn used as a cheap surrogate model for further studies. We introduce two specific RADIS implementations that use Gaussian Processes (GPs) and Nearest Neighbors (NN) for constructing the emulator. Several numerical experiments and comparisons show the benefits of the proposed schemes. A real-world application in remote sensing model inversion and emulation confirms the validity of the approach.