# Layered Adaptive Importance Sampling

arXiv: https://arxiv.org/abs/1505.04732 · HTML: https://mlsanity.com/paper/1505.04732/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2015.

## Built on by (most cited first, 18 of 18)

- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [Automatic tempered posterior distributions for Bayesian inversion problems](https://mlsanity.com/paper/2107.11614/) (2021)
- [MCMC-driven importance samplers](https://mlsanity.com/paper/2105.02579/) (2021)
- [Compressed Monte Carlo with application in particle filtering](https://mlsanity.com/paper/2107.08459/) (2021)
- [Adaptive importance sampling for heavy-tailed distributions via α-divergence minimization](https://mlsanity.com/paper/2310.16653/) (2023)
- [Global convergence of optimized adaptive importance samplers](https://mlsanity.com/paper/2201.00409/) (2022)
- [A Quadrature Rule combining Control Variates and Adaptive Importance Sampling](https://mlsanity.com/paper/2205.11890/) (2022)
- [Hamiltonian Adaptive Importance Sampling](https://mlsanity.com/paper/2209.13716/) (2022)
- [Efficient Bayes Inference in Neural Networks through Adaptive Importance Sampling](https://mlsanity.com/paper/2210.00993/) (2022)
- [A Deep Reinforcement Learning Approach to Rare Event Estimation](https://mlsanity.com/paper/2211.12470/) (2022)
- [Rethinking Variational Inference for Probabilistic Programs with Stochastic Support](https://mlsanity.com/paper/2311.00594/) (2023)
- [Meta-Learning an Inference Algorithm for Probabilistic Programs](https://mlsanity.com/paper/2103.00737/) (2021)
- [Inference over radiative transfer models using variational and expectation maximization methods](https://mlsanity.com/paper/2204.03346/) (2022)
- [Adaptively Optimised Adaptive Importance Samplers](https://mlsanity.com/paper/2307.09341/) (2023)
- [Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals](https://mlsanity.com/paper/2501.01148/) (2025)
- [How to Approximate Inference with Subtractive Mixture Models](https://mlsanity.com/paper/2604.16714/) (2026)
- [Beyond Bayesian Model Averaging over Paths in Probabilistic Programs with Stochastic Support](https://mlsanity.com/paper/2310.14888/) (2023)
- [Deterministic Fokker-Planck Transport -- With Applications to Sampling, Variational Inference, Kernel Mean Embeddings & Sequential Monte Carlo](https://mlsanity.com/paper/2410.18993/) (2024)

## Abstract (arXiv)

Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler proposal probability densities to draw candidate samples. The performance of any such method is strictly related to the specification of the proposal distribution, such that unfortunate choices easily wreak havoc on the resulting estimators. In this work, we introduce a layered (i.e., hierarchical) procedure to generate samples employed within a Monte Carlo scheme. This approach ensures that an appropriate equivalent proposal density is always obtained automatically (thus eliminating the risk of a catastrophic performance), although at the expense of a moderate increase in the complexity. Furthermore, we provide a general unified importance sampling (IS) framework, where multiple proposal densities are employed and several IS schemes are introduced by applying the so-called deterministic mixture approach. Finally, given these schemes, we also propose a novel class of adaptive importance samplers using a population of proposals, where the adaptation is driven by independent parallel or interacting Markov Chain Monte Carlo (MCMC) chains. The resulting algorithms efficiently combine the benefits of both IS and MCMC methods.