# Nested Sequential Monte Carlo Methods

arXiv: https://arxiv.org/abs/1502.02536 · HTML: https://mlsanity.com/paper/1502.02536/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2015.

## Built on by (most cited first, 19 of 19)

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- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
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- [Differentiable Particle Filtering without Modifying the Forward Pass](https://mlsanity.com/paper/2106.10314/) (2021)
- [Nested Variational Inference](https://mlsanity.com/paper/2106.11302/) (2021)
- [Illusory Attacks: Information-Theoretic Detectability Matters in Adversarial Attacks](https://mlsanity.com/paper/2207.10170/) (2022)
- [Variational Combinatorial Sequential Monte Carlo Methods for Bayesian Phylogenetic Inference](https://mlsanity.com/paper/2106.00075/) (2021)
- [Recursive Monte Carlo and Variational Inference with Auxiliary Variables](https://mlsanity.com/paper/2203.02836/) (2022)
- [Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2606.15576/) (2026)
- [Learning Proposals for Probabilistic Programs with Inference Combinators](https://mlsanity.com/paper/2103.00668/) (2021)
- [Variational Marginal Particle Filters](https://mlsanity.com/paper/2109.15134/) (2021)
- [NAS-X: Neural Adaptive Smoothing via Twisting](https://mlsanity.com/paper/2308.14864/) (2023)
- [Divide-and-Conquer Predictive Coding: a structured Bayesian inference algorithm](https://mlsanity.com/paper/2408.05834/) (2024)
- [Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space](https://mlsanity.com/paper/2501.17965/) (2025)
- [Optimization of Annealed Importance Sampling Hyperparameters](https://mlsanity.com/paper/2209.13226/) (2022)
- [Discrete Diffusion Inference-Time Control with Nested Sequential Monte Carlo](https://mlsanity.com/paper/2608.20123/) (2026)
- [String Diagrams with Factorized Densities](https://mlsanity.com/paper/2305.02506/) (2023)
- [Nonlinear Bayesian Estimator for Parameter Learning: A Fixed-Point Characterization](https://mlsanity.com/paper/2606.10111/) (2026)

## Abstract (arXiv)

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. Furthermore, NSMC can in itself be used to produce such properly weighted samples. Consequently, one NSMC sampler can be used to construct an efficient high-dimensional proposal distribution for another NSMC sampler, and this nesting of the algorithm can be done to an arbitrary degree. This allows us to consider complex and high-dimensional models using SMC. We show results that motivate the efficacy of our approach on several filtering problems with dimensions in the order of 100 to 1 000.