Improving multiple-try Metropolis with local balancing

• URL: http://arxiv.org/abs/2211.11613v2
• Date: Thu, 24 Aug 2023 01:04:03 GMT
• Title: Improving multiple-try Metropolis with local balancing
• Authors: Philippe Gagnon, Florian Maire, Giacomo Zanella
• Abstract summary: Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo method. We show both theoretically and empirically that this weight function induces pathological behaviours in high dimensions. We propose to instead use weight functions akin to the locally-balanced proposal distributions of Zanella ( 2020)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo method with the appealing feature of being amenable to parallel computing. At each iteration, it samples several candidates for the next state of the Markov chain and randomly selects one of them based on a weight function. The canonical weight function is proportional to the target density. We show both theoretically and empirically that this weight function induces pathological behaviours in high dimensions, especially during the convergence phase. We propose to instead use weight functions akin to the locally-balanced proposal distributions of Zanella (2020), thus yielding MTM algorithms that do not exhibit those pathological behaviours. To theoretically analyse these algorithms, we study the high-dimensional performance of ideal schemes that can be thought of as MTM algorithms which sample an infinite number of candidates at each iteration, as well as the discrepancy between such schemes and the MTM algorithms which sample a finite number of candidates. Our analysis unveils a strong distinction between the convergence and stationary phases: in the former, local balancing is crucial and effective to achieve fast convergence, while in the latter, the canonical and novel weight functions yield similar performance. Numerical experiments include an application in precision medicine involving a computationally-expensive forward model, which makes the use of parallel computing within MTM iterations beneficial.

Related papers

• Sample-Efficient Multi-Agent RL: An Optimization Perspective [103.35353196535544]
  We study multi-agent reinforcement learning (MARL) for the general-sum Markov Games (MGs) under the general function approximation. We introduce a novel complexity measure called the Multi-Agent Decoupling Coefficient (MADC) for general-sum MGs. We show that our algorithm provides comparable sublinear regret to the existing works.
  arXiv  Detail & Related papers  (2023-10-10T01:39:04Z)
• Federated Conditional Stochastic Optimization [110.513884892319]
  Conditional optimization has found in a wide range of machine learning tasks, such as in-variant learning tasks, AUPRC, andAML. This paper proposes algorithms for distributed federated learning.
  arXiv  Detail & Related papers  (2023-10-04T01:47:37Z)
• Stochastic Gradient Descent-like relaxation is equivalent to Metropolis dynamics in discrete optimization and inference problems [0.7499722271664147]
  We show that the dynamics of an SGD-like algorithm resemble very closely that of Metropolis Monte Carlo with a properly chosen temperature. This equivalence allows us to use results about performances and limits of Monte Carlo algorithms to optimize the mini-batch size in the SGD-like algorithm.
  arXiv  Detail & Related papers  (2023-09-11T09:34:44Z)
• SpreadNUTS -- Moderate Dynamic Extension of Paths for No-U-Turn Sampling & Partitioning Visited Regions [0.0]
  This paper introduces modifications to a specific Hamiltonian Monte Carlo (HMC) algorithm known as the no-U-turn sampler (NUTS) NUTS aims to explore the sample space faster than NUTS, yielding a sampler that has faster convergence to the true distribution than NUTS.
  arXiv  Detail & Related papers  (2023-07-09T05:00:25Z)
• PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash Equilibrium [62.51015395213579]
  We consider the non-AL equilibrium nonconptotic objective function in two-player zero-sum continuous games. The proposed algorithm employs the movements of particles to represent the updates of random strategies for the $ilon$-mixed Nash equilibrium.
  arXiv  Detail & Related papers  (2023-03-02T05:08:15Z)
• A Stochastic Newton Algorithm for Distributed Convex Optimization [62.20732134991661]
  We analyze a Newton algorithm for homogeneous distributed convex optimization, where each machine can calculate gradients of the same population objective. We show that our method can reduce the number, and frequency, of required communication rounds compared to existing methods without hurting performance.
  arXiv  Detail & Related papers  (2021-10-07T17:51:10Z)
• Efficient semidefinite-programming-based inference for binary and multi-class MRFs [83.09715052229782]
  We propose an efficient method for computing the partition function or MAP estimate in a pairwise MRF. We extend semidefinite relaxations from the typical binary MRF to the full multi-class setting, and develop a compact semidefinite relaxation that can again be solved efficiently using the solver.
  arXiv  Detail & Related papers  (2020-12-04T15:36:29Z)
• An adaptive Hessian approximated stochastic gradient MCMC method [12.93317525451798]
  We present an adaptive Hessian approximated gradient MCMC method to incorporate local geometric information while sampling from the posterior. We adopt a magnitude-based weight pruning method to enforce the sparsity of the network.
  arXiv  Detail & Related papers  (2020-10-03T16:22:15Z)
• Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors [8.11978827493967]
  We propose an approach using parallel runs of MCMC, variational, or mode-based inference to hit as many modes as possible. We present theoretical consistency with an example where the stacked inference process approximates the true data. We demonstrate practical implementation in several model families.
  arXiv  Detail & Related papers  (2020-06-22T15:26:59Z)
• Theoretical Convergence of Multi-Step Model-Agnostic Meta-Learning [63.64636047748605]
  We develop a new theoretical framework to provide convergence guarantee for the general multi-step MAML algorithm. In particular, our results suggest that an inner-stage step needs to be chosen inversely proportional to $N$ of inner-stage steps in order for $N$ MAML to have guaranteed convergence.
  arXiv  Detail & Related papers  (2020-02-18T19:17:54Z)
• Ensemble Slice Sampling: Parallel, black-box and gradient-free inference for correlated & multimodal distributions [0.0]
  Slice Sampling has emerged as a powerful Markov Chain Monte Carlo algorithm that adapts to the characteristics of the target distribution with minimal hand-tuning. This paper introduces Ensemble Slice Sampling (ESS), a new class of algorithms that bypasses such difficulties by adaptively tuning the initial length scale. These affine-invariant algorithms are trivial to construct, require no hand-tuning, and can easily be implemented in parallel computing environments.
  arXiv  Detail & Related papers  (2020-02-14T19:00:12Z)

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.