# Variational autoencoder with weighted samples for high-dimensional non-parametric adaptive importance sampling

arXiv: https://arxiv.org/abs/2310.09194 · HTML: https://mlsanity.com/paper/2310.09194/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 95 references that are in the map.
- First posted on arXiv 13 Oct 2023.

## Builds on (most cited first, 19 of 19)

- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Lagging Inference Networks and Posterior Collapse in Variational Autoencoders](https://mlsanity.com/paper/1901.05534/) (2019)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [Spherical Latent Spaces for Stable Variational Autoencoders](https://mlsanity.com/paper/1808.10805/) (2018)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Variational Autoencoders with Riemannian Brownian Motion Priors](https://mlsanity.com/paper/2002.05227/) (2020)
- [Variational Autoencoder with Implicit Optimal Priors](https://mlsanity.com/paper/1809.05284/) (2018)
- [i-flow: High-dimensional Integration and Sampling with Normalizing Flows](https://mlsanity.com/paper/2001.05486/) (2020)
- [Improving VAE generations of multimodal data through data-dependent conditional priors](https://mlsanity.com/paper/1911.10885/) (2019)

## Built on by (most cited first, 3 of 3)

- [Optimal Demixing of Nonparametric Densities](https://mlsanity.com/paper/2603.27457/) (2026)
- [Scalable Importance Sampling in High Dimensions with Low-Rank Mixture Proposals](https://mlsanity.com/paper/2505.13335/) (2025)
- [Global Sensitivity Analysis for Engineering Design Based on Individual Conditional Expectations](https://mlsanity.com/paper/2512.11946/) (2025)

## Abstract (arXiv)

Probability density function estimation with weighted samples is the main foundation of all adaptive importance sampling algorithms. Classically, a target distribution is approximated either by a non-parametric model or within a parametric family. However, these models suffer from the curse of dimensionality or from their lack of flexibility. In this contribution, we suggest to use as the approximating model a distribution parameterised by a variational autoencoder. We extend the existing framework to the case of weighted samples by introducing a new objective function. The flexibility of the obtained family of distributions makes it as expressive as a non-parametric model, and despite the very high number of parameters to estimate, this family is much more efficient in high dimension than the classical Gaussian or Gaussian mixture families. Moreover, in order to add flexibility to the model and to be able to learn multimodal distributions, we consider a learnable prior distribution for the variational autoencoder latent variables. We also introduce a new pre-training procedure for the variational autoencoder to find good starting weights of the neural networks to prevent as much as possible the posterior collapse phenomenon to happen. At last, we explicit how the resulting distribution can be combined with importance sampling, and we exploit the proposed procedure in existing adaptive importance sampling algorithms to draw points from a target distribution and to estimate a rare event probability in high dimension on two multimodal problems.