# Hess-MC2: Sequential Monte Carlo Squared using Hessian Information and Second Order Proposals

arXiv: https://arxiv.org/abs/2507.07461 · HTML: https://mlsanity.com/paper/2507.07461/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Particle Filter Networks with Application to Visual Localization](https://mlsanity.com/paper/1805.08975/) (2018)
- [Differentiable Particle Filtering via Entropy-Regularized Optimal Transport](https://mlsanity.com/paper/2102.07850/) (2021)
- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters](https://mlsanity.com/paper/2111.01409/) (2021)
- [Tuning Sequential Monte Carlo Samplers via Greedy Incremental Divergence Minimization](https://mlsanity.com/paper/2503.15704/) (2025)
- [Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models](https://mlsanity.com/paper/1511.01707/) (2015)
- [Particle Metropolis-Hastings using gradient and Hessian information](https://mlsanity.com/paper/1311.0686/) (2013)
- [Enhanced SMC2: Leveraging Gradient Information from Differentiable Particle Filters Within Langevin Proposals](https://mlsanity.com/paper/2407.17296/) (2024)
- [Particle Metropolis-adjusted Langevin algorithms](https://mlsanity.com/paper/1412.7299/) (2014)
- [Incorporating the ChEES Criterion into Sequential Monte Carlo Samplers](https://mlsanity.com/paper/2504.02627/) (2025)
- [Particle approximations of the score and observed information matrix for parameter estimation in state space models with linear computational cost](https://mlsanity.com/paper/1306.0735/) (2013)

## Built on by (most cited first, 1 of 1)

- [Investigating Batch Inference in a Sequential Monte Carlo Framework for Neural Networks](https://mlsanity.com/paper/2601.21983/) (2026)

## Abstract (arXiv)

When performing Bayesian inference using Sequential Monte Carlo (SMC) methods, two considerations arise: the accuracy of the posterior approximation and computational efficiency. To address computational demands, Sequential Monte Carlo Squared (SMC2) is well-suited for high-performance computing (HPC) environments. The design of the proposal distribution within SMC2 can improve accuracy and exploration of the posterior as poor proposals may lead to high variance in importance weights and particle degeneracy. The Metropolis-Adjusted Langevin Algorithm (MALA) uses gradient information so that particles preferentially explore regions of higher probability. In this paper, we extend this idea by incorporating second-order information, specifically the Hessian of the log-target. While second-order proposals have been explored previously in particle Markov Chain Monte Carlo (p-MCMC) methods, we are the first to introduce them within the SMC2 framework. Second-order proposals not only use the gradient (first-order derivative), but also the curvature (second-order derivative) of the target distribution. Experimental results on synthetic models highlight the benefits of our approach in terms of step-size selection and posterior approximation accuracy when compared to other proposals.