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

• URL: http://arxiv.org/abs/2507.07461v1
• Date: Thu, 10 Jul 2025 06:26:54 GMT
• Title: Hess-MC2: Sequential Monte Carlo Squared using Hessian Information and Second Order Proposals
• Authors: Joshua Murphy, Conor Rosato, Andrew Millard, Lee Devlin, Paul Horridge, Simon Maskell,
• Abstract summary: We introduce second-order proposals within the Sequential Monte Carlo Squared (SMC$2$) framework.<n>In this paper, we extend this idea by incorporating second-order information, specifically the Hessian of the log-target.<n>Results on synthetic models highlight the benefits of our approach in terms of step-size selection and posterior approximation accuracy.
• Score: 2.170477444239546
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 (SMC$^2$) is well-suited for high-performance computing (HPC) environments. The design of the proposal distribution within SMC$^2$ 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 SMC$^2$ 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.

Related papers

• Sliced Wasserstein with Random-Path Projecting Directions [49.802024788196434]
  We propose an optimization-free slicing distribution that provides a fast sampling for the Monte Carlo estimation of expectation. We derive the random-path slicing distribution (RPSD) and two variants of sliced Wasserstein, i.e., the Random-Path Projection Sliced Wasserstein (RPSW) and the Importance Weighted Random-Path Projection Sliced Wasserstein (IWRPSW)
  arXiv  Detail & Related papers  (2024-01-29T04:59:30Z)
• Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo [104.9535542833054]
  We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL) We instead directly sample the Q function from its posterior distribution, by using Langevin Monte Carlo. Our approach achieves better or similar results compared with state-of-the-art deep RL algorithms on several challenging exploration tasks from the Atari57 suite.
  arXiv  Detail & Related papers  (2023-05-29T17:11:28Z)
• Towards Practical Preferential Bayesian Optimization with Skew Gaussian Processes [8.198195852439946]
  We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. We develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.
  arXiv  Detail & Related papers  (2023-02-03T03:02:38Z)
• A Two-step Metropolis Hastings Method for Bayesian Empirical Likelihood Computation with Application to Bayesian Model Selection [0.0]
  We propose a two-step reversible Monte Carlo algorithm to sample from a set posterior of a Markov chain. We also discuss empirical likelihood and extend our two-step reversible Monte Carlo algorithm to a jump chain procedure to sample from the resulting set.
  arXiv  Detail & Related papers  (2022-09-02T20:40:21Z)
• The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distribution [1.1279808969568252]
  Current state-of-the-art methods often address these difficulties by replacing the posterior density with a smooth approximation. An alternative approach is based on data augmentation and relaxation, where auxiliary variables are introduced in order to construct an approximate augmented posterior distribution. This paper proposes a new accelerated proximal MCMC method called latent space SK-ROCK, which tightly combines the benefits of the two strategies.
  arXiv  Detail & Related papers  (2022-06-28T11:21:41Z)
• Langevin Monte Carlo for Contextual Bandits [72.00524614312002]
  Langevin Monte Carlo Thompson Sampling (LMC-TS) is proposed to directly sample from the posterior distribution in contextual bandits. We prove that the proposed algorithm achieves the same sublinear regret bound as the best Thompson sampling algorithms for a special case of contextual bandits.
  arXiv  Detail & Related papers  (2022-06-22T17:58:23Z)
• De-Sequentialized Monte Carlo: a parallel-in-time particle smoother [3.97478982737167]
  We propose dSMC (de-Sequentialized Monte Carlo), a new particle smoother that is able to process $T$ observations in $mathcalO(log T)$ time. This compares favourably with standard particle smoothers, the complexity of which is linear in $T$. We also design a particle Gibbs sampler based on dSMC, which is able to perform parameter inference in a state-space model at a $mathcalO(log(T))$ cost on parallel hardware.
  arXiv  Detail & Related papers  (2022-02-04T17:46:32Z)
• Mean-Square Analysis with An Application to Optimal Dimension Dependence of Langevin Monte Carlo [60.785586069299356]
  This work provides a general framework for the non-asymotic analysis of sampling error in 2-Wasserstein distance. Our theoretical analysis is further validated by numerical experiments.
  arXiv  Detail & Related papers  (2021-09-08T18:00:05Z)
• What Are Bayesian Neural Network Posteriors Really Like? [63.950151520585024]
  We show that Hamiltonian Monte Carlo can achieve significant performance gains over standard and deep ensembles. We also show that deep distributions are similarly close to HMC as standard SGLD, and closer than standard variational inference.
  arXiv  Detail & Related papers  (2021-04-29T15:38:46Z)
• Distributed Averaging Methods for Randomized Second Order Optimization [54.51566432934556]
  We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization that employ sampling and sketching of the Hessian. We also extend the framework of second order averaging methods to introduce an unbiased distributed optimization framework for heterogeneous computing systems.
  arXiv  Detail & Related papers  (2020-02-16T09:01:18Z)
• DDKSP: A Data-Driven Stochastic Programming Framework for Car-Sharing Relocation Problem [17.440172040605354]
  We investigate the car-sharing relocation problem (CSRP) under uncertain demands. In order to overcome the problem, an innovative framework called Data-Driven Kernel Programming (DDKSP) is proposed. The proposed framework outperforms the pure parametric approaches with 3.72%, 4.58% and 11% in terms of overall profits.
  arXiv  Detail & Related papers  (2020-01-20T19:04:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.