We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method based on an interacting pool of standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler on an extended space. We present empirical results that show significant improv…
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48 results for “Monte Carlo samplers”
New samplers improve MCMC efficiency in high dimensions.
problem Efficient sampling in high-dimensional problems.
method Affine invariant ensemble samplers, including derivative-free and derivative-based HMC.
result Affine invariant ensemble HMC outperforms standard HMC in high dimensions.
New method corrects bias in stochastic gradient samplers.
problem Bias in stochastic gradient samplers.
method Gradient-Guided Monte Carlo with stochastic gradients.
result Corrected sampler yields nonzero acceptance probabilities.
ChEES-HMC improves SMC samplers' efficiency and speed.
problem Efficiently sampling from complex posterior distributions.
method Incorporating ChEES-HMC into SMC samplers.
result ChEES-HMC outperforms NUTS in speed and efficiency.
New method tunes SMC samplers efficiently without high costs.
problem Tuning SMC samplers with unadjusted kernels is challenging.
method Greedy Incremental Divergence Minimization (GIDM) for step size tuning.
result GIDM reduces KL divergence and tunes SMC samplers efficiently.
Randomized Runge-Kutta-Nyström Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlomath.NA
New methods improve efficiency of sampling algorithms for complex systems.
problem Efficiently sampling from complex, high-dimensional probability distributions.
method Randomized Runge-Kutta-Nyström methods tailored for Hamiltonian flows.
result Quantitative -order -accuracy in approximating Hamiltonian flows.
New study on No-U-Turn Sampler for accelerated mixing in Hamiltonian Monte Carlo.
problem Achieving accelerated convergence in Hamiltonian Monte Carlo.
method Combining concentration of measure and coupling analysis for mixing.
result Rigorous mixing guarantees for the No-U-Turn Sampler in certain Gaussian distributions.
Enhanced Markov chain sampler learns network statistics faster.
problem Learning network statistics efficiently.
method Integrates graph Forman curvature into Markov chain transition probabilities and stationary distribution.
result Curved Markov chain Monte Carlo achieves faster convergence.
GIST adapts HMC by tuning parameters based on position and momentum.
problem Locally adaptive sampling in Hamiltonian Monte Carlo.
method GIST uses Gibbs sampling to adaptively tune HMC parameters.
result GIST improves sampling efficiency for high-dimensional models.
Improved efficiency in HMC samplers reduces dissipative behavior.
problem Reducing dissipative behavior in HMC samplers.
method Variable integration time and partial velocity refreshment.
result Efficiency improved by a √κ factor in Wasserstein-2 distance.
CRAFT improves on existing methods for sampling complex distributions.
problem Sampling from complex probability distributions.
method Combines SMC with variational inference using normalizing flows.
result Improves on Annealed Flow Transport Monte Carlo and MCMC-based Stochastic Normalizing Flows.
Paper proposes a new method for sampling from complex distributions.
problem Sampling from unnormalised density functions in complex distributions.
method Combines amortised and particle-based methods with reinforcement learning.
result Improves sampling from complex distributions compared to existing methods.
Ray tracing sampler improves neural network sampling efficiency and resilience.
problem Sampling neural network posterior distributions efficiently and robustly.
method Markov Chain Monte Carlo using ray tracing through likelihood space.
result Significantly higher resilience to gradient heating compared to HMC.
GPU-accelerated particle methods outperform neural samplers in LFT benchmarks.
problem High-dimensional multimodal sampling problems in lattice field theory.
method GPU-accelerated particle Monte Carlo methods (Sequential Monte Carlo and nested sampling).
result These methods match or outperform neural samplers in sample quality and wall-clock time.
A new sampler tackles critical phenomena by leveraging scale invariance.
problem Scale invariance at criticality causes sampling difficulties in Monte Carlo simulations.
method RiGCS combines MLMC-HB with generative models to improve sampling efficiency.
result RiGCS achieves significantly higher effective sample size than existing methods.
New SMC sampler improves diffusion model sampling efficiency.
problem Sampling generative diffusion models efficiently.
method Constructs correlated observation paths and designs a sampler.
result Improved statistical efficiency, especially under outlier conditions.
Generative Neural Samplers for the Quantum Heisenberg Chaincond-mat.stat-mech
Generative neural samplers estimate quantum spin system properties.
problem Estimating observables for quantum spin systems.
method Autoregressive models using Suzuki-Trotter transformation.
result Results for energy, specific heat, and susceptibility are in good agreement with Monte Carlo methods.
Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC…
Develops diffusion samplers for target distributions with efficient score and density estimates.
problem Estimating scores and densities for time-varying distributions.
method Sequential Monte Carlo with diffusion paths and control variates.
result Effective samplers for time-varying distributions with theoretical guarantees and practical applications.
New SMC samplers improve stochastic optimisation efficiency.
problem Optimizing functions with intractable gradients in machine learning and statistics.
method Sequential Monte Carlo (SMC) samplers for stochastic optimisation.
result Significant computational gains achieved with SMC approximations.
We explore a general framework in Markov chain Monte Carlo (MCMC) sampling where sequential proposals are tried as a candidate for the next state of the Markov chain. This sequential-proposal framework can be applied to various existing MCMC methods, including Metropolis-Hastings algorithms using random proposals and m…
Bayesian inference for factorial hidden Markov models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often restricted to exploration around localised regions that depend on initialisation. We …
Improved state estimation in high-dimensional models using Zig-Zag Sampler.
problem Weight degeneracy in particle filtering methods for high-dimensional state space models.
method Discrete Zig-Zag Sampler applied within the Composite MH Kernel of SMCMC framework.
result Improves estimation accuracy and increases acceptance ratio in high-dimensional state estimation.
We present a novel technique for learning the mass matrices in samplers obtained from discretized dynamics that preserve some energy function. Existing adaptive samplers use Riemannian preconditioning techniques, where the mass matrices are functions of the parameters being sampled. This leads to significant complexiti…
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings, produce output samples drawn from a distribution that may be far from the target …
We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS). We provide a theoretical anal…
The paper proposes a Gibbs sampler for neural network posterior sampling.
problem Sampling from the posterior of neural networks.
method Adding noise to activations and using a Gibbs sampler.
result The Gibbs sampler achieves similar performance to MCMC methods on real and synthetic data.
Improves MCMC performance with adaptive affine transformations.
problem Improving the performance of Markov Chain Monte Carlo samplers.
method Adaptive learning of bijective affine transformations during sampling.
result Adaptive affine transformations improve the quality of samples at low computational cost.
New method for MCMC models without perfect or sequential samplers.
problem Bayesian inference for complex models with intractable terms.
method Utilizes tractable independence model to construct unbiased estimates.
result Scalable method for high-dimensional models.
SRO optimizes decisions against worst-case sampler induced by generative models.
problem Operational uncertainty shifts from explicit probability law to sampler induced by learned generators.
method SRO optimizes decisions against the worst-case sampler induced by perturbing the learned generator.
result Empirical worst-case objective provides high-probability upper certificate for true population objective.
ABC Samplersstat.CO
This Chapter, "ABC Samplers", is to appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and algorithms used to sample from the ABC approximation to the posterior distribution, including methods based on rejection/importance sampling, MCMC and sequential Monte Carlo.
Paper reviews methods for conditional sampling in generative diffusion models.
problem Extending generative diffusion models to sample from conditional distributions.
method Review of existing computational approaches to conditional sampling.
result Highlight key methodologies for constructing conditional generative samplers.
DNFS trains efficient samplers for discrete distributions using locally equivariant Transformers.
problem Sampling from unnormalised discrete distributions.
method DNFS learns a rate matrix to satisfy the Kolmogorov equation, using control variates and locally equivariant Transformers.
result DNFS achieves efficient and effective sampling across various applications.
Parallelizes active learning for Bayesian inference using Nested Sampler.
problem Expensive likelihood evaluations in complex experiments.
method Uses Nested Sampler to generate nearly-optimal batches of candidates in parallel.
result Comparable accuracy to sequential conditioning with efficient parallelization.
The Bouncy Particle Sampler is a novel rejection-free non-reversible sampler for differentiable probability distributions over continuous variables. We generalize the algorithm to piecewise differentiable distributions and apply it to generic binary distributions using a piecewise differentiable augmentation. We illust…
New algorithms improve MCMC efficiency for complex distributions.
problem High variance and low effective sample size in MCMC samplers.
method Antithetic Riemannian Manifold and Quantum-Inspired Hamiltonian Monte Carlo.
result Improved effective sample size and variance reduction.
CMCD sampler connects transport and variational inference for efficient sampling.
problem Efficient sampling and generative modeling in Bayesian computation.
method Developed a principled framework using divergences on path space, CMCD sampler with adaptive dynamics.
result CMCD sampler outperforms competing approaches across various experiments.
In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare eve…
On the convergence of dynamic implementations of Hamiltonian Monte Carlo and No U-Turn Samplersstat.CO
This paper analyzes the convergence of dynamic HMC and NUTS methods.
problem Theoretical understanding of dynamic HMC and NUTS convergence.
method General class of MCMC algorithms, NUTS as a particular case, geometric ergodicity, irreducibility.
result NUTS is geometrically ergodic under certain conditions and ergodic without bounded stepsize.
Gibbs sampler contracts entropy under strong log-concavity, improving mixing time.
problem Improving the mixing time of Gibbs sampler under strong log-concavity.
method Analyzing Gibbs sampler contraction under strong log-concavity, providing sharp contraction rate.
result Gibbs sampler contracts entropy linearly with condition number and independent of dimension under strong log-concavity.
This paper analyzes error bounds for biased SMC samplers in conditional sampling.
problem Analyzing error bounds for biased SMC samplers in conditional sampling.
method Develops a non-asymptotic error analysis for SMC samplers with biased mutation kernels.
result Derives the first non-asymptotic error bound for conditional sampling with score-based diffusion models.
ParaMonte::Python streamlines Bayesian data analysis with fast Monte Carlo and MCMC routines.
problem Efficiently sampling posterior distributions in Bayesian modeling and data science.
method Serial and MPI-parallelized Markov Chain Monte Carlo (MCMC) routines.
result Automated model calibration and uncertainty quantification in Bayesian analysis.
ParaMonte: A high-performance serial/parallel Monte Carlo simulation library for C, C++, Fortrancs.MS
ParaMonte simplifies Monte Carlo simulations for various scientific fields.
problem Efficiently performing Monte Carlo simulations for complex models.
method Unified, high-performance, parallelized library for C, C++, Fortran.
result Automates and streamlines Monte Carlo sampling for arbitrary-dimensional functions.
New MCMC methods map high-dimensional problems to spheres for better mixing.
problem Mixing issues in high-dimensional distributions, especially heavy-tailed ones.
method Stereographic Markov Chain Monte Carlo (MCMC) methods that map high-dimensional problems to spheres.
result Uniformly ergodic samplers for various distributions, including heavy-tailed ones, with faster convergence in higher dimensions.
WALNUTS improves sampling efficiency and robustness for multi-scale distributions.
problem Adapting leapfrog step size for multi-scale posterior distributions.
method Adapts leapfrog step size at fixed intervals of simulated time, selecting the largest step size to keep energy error below a threshold.
result Substantial improvements in sampling efficiency and robustness compared to standard NUTS.
Gradient boosting can be seen as Gaussian process inference.
problem Improving uncertainty estimates in out-of-domain detection.
method Gradient boosting reformulated as a kernel method converging to Gaussian process inference.
result Gradient boosting can provide better uncertainty estimates through Monte-Carlo estimation of posterior variance.
New PDMP samplers tackle variable selection in models.
problem Jointly explore model space and parameter space.
method Develop reversible jump PDMP samplers.
result New samplers mix better and are more efficient.
Improved Bayesian analysis for SVM models using a mixture sampler.
problem Efficient simulation-based analysis of stochastic volatility in mean models.
method Developed a generalized mixture sampler for SVM models, approximating non-central chi-squared distributions as mixtures of normal distributions.
result The proposed method outperforms other volatility models based on marginal likelihoods in empirical studies.