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.
This work analyzes Gibbs samplers for Bayesian hierarchical models without dimensionality constraints.
problem Analyzing convergence properties of Gibbs samplers for Bayesian hierarchical models.
method Using Bayesian asymptotics and total variation mixing times, the study provides dimension-free convergence results.
result Dimension-free convergence results for Gibbs samplers targeting hierarchical models under random data-generating assumptions.
New SMC method for pBNNs improves scalability and predictive performance.
problem Training pBNNs with high-dimensional stochastic parameters.
method Gradient-based proposals within SMC samplers.
result New method outperforms state-of-the-art in predictive performance and training time.
Enhances gradient-based discrete samplers with parallel tempering for multimodal distributions.
problem Local minima in high-dimensional, multimodal discrete distributions.
method Combines parallel tempering with discrete Langevin proposal, using Metropolis criterion for swaps.
result Significantly faster mixing and better sampling from complex distributions.
New sampler tackles complex discrete energy landscapes efficiently.
problem Stagnation in gradient-based discrete samplers for non-convex settings.
method DREXEL sampler with Replica Exchange and Adjusted Metropolis.
result Proves samplers satisfy detailed balance and converge to target distribution.
Gradient-based MCMC for discrete spaces improves sampling performance.
problem Sampling in discrete spaces using traditional methods is challenging.
method Introduced new discrete Metropolis-Hastings samplers inspired by MALA, with a novel preconditioning technique.
result Demonstrated strong empirical performance across various challenging sampling problems.
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.
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.
We introduce a novel stochastic version of the non-reversible, rejection-free Bouncy Particle Sampler (BPS), a Markov process whose sample trajectories are piecewise linear. The algorithm is based on simulating first arrival times in a doubly stochastic Poisson process using the thinning method, and allows efficient sa…
RLMH improves adaptive MCMC by optimizing contrastive divergence reward.
problem Tuning MCMC samplers is challenging and time-consuming.
method Formulated Metropolis-Hastings as a Markov decision process and used RL to adaptively tune it.
result A novel reward function based on contrastive divergence outperforms existing ones.
We introduce a new family of MCMC samplers that combine auxiliary variables, Gibbs sampling and Taylor expansions of the target density. Our approach permits the marginalisation over the auxiliary variables yielding marginal samplers, or the augmentation of the auxiliary variables, yielding auxiliary samplers. The well…
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.
A new sampler for complex discrete distributions efficiently updates all variables in parallel.
problem Sampling complex high-dimensional discrete distributions efficiently and accurately.
method Discrete Langevin proposal (DLP) for parallel coordinate updates with controlled stepsize.
result DLP efficiently explores high-dimensional and strongly correlated variables with asymptotic bias of zero for log-quadratic distributions.
PDHAMS improves sampling for discrete distributions with quadratic potential functions.
problem Sampling discrete distributions efficiently and accurately.
method Integrates a second-order approximation of the potential function and uses Gaussian integral trick.
result PDHAMS yields superior performance compared to other methods.
Statistical finite elements use Langevin dynamics to efficiently handle uncertainty quantification.
problem Uncertainty quantification in finite element models with observed data.
method Langevin dynamics, unadjusted Langevin algorithm (ULA), for sampling posterior distributions.
result ULA provides a scalable and efficient method for characterizing the posterior distribution of statFEM models.
Develops algorithm to differentiate Metropolis-Hastings for optimization.
problem Optimizing intractable densities with discrete components.
method Fuses stochastic automatic differentiation with Markov chain coupling schemes.
result Unbiased and low-variance gradient estimator for intractable densities.
HiSS sampling overcomes local mode traps in rugged discrete spaces.
problem Sampling multimodal discrete distributions with gradient-based methods.
method Integrates Metropolis-within-Gibbs framework with logistic convolution.
result HiSS outperforms alternatives on various tasks, including Ising models and binary neural networks.
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth order optimization algorithm which demands only t…
Exact posterior score estimation for solving linear inverse problems
problem Solving linear inverse problems
method Derive the exact posterior score and use it as a denoising training objective
result EPS outperforms training-free and training-based baselines on various metrics
Bayesian framework reduces online optimization regret.
problem Sequential optimization in dynamic environments with bounded losses.
method PAC-Bayes theory and Bayesian updating principles.
result Achieves O ( T ) \mathcal{O}(\sqrt{T}) O ( T ) regret for bounded losses. Corrected samplers reduce discretization error in discrete flow models without additional computational cost.
problem Discretization error in samplers for discrete flow models.
method Established non-asymptotic error bounds for samplers, proposed time-corrected and location-corrected samplers.
result Location-corrected sampler has lower complexity and better generation quality.
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 study shows Gaussian samplers struggle with heavy-tailed targets, while stable samplers excel.
problem The difficulty of sampling from heavy-tailed distributions using Gaussian versus stable oracles.
method Comparison of Gaussian and stable oracles for proximal samplers.
result Gaussian samplers have a fundamental barrier for high-accuracy guarantees in heavy-tailed sampling, while stable samplers excel.
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.
PAC-Bayesian matrix completion with a spectral scaled Student prior offers efficient inference.
problem Matrix completion with underlying low-rank structure.
method Spectral scaled Student prior and PAC-Bayesian bounds.
result Minimax-optimal oracle inequality for model misspecification and general sampling distribution.
The Gibbs sampler is a particularly popular Markov chain used for learning and inference problems in Graphical Models (GMs). These tasks are computationally intractable in general, and the Gibbs sampler often suffers from slow mixing. In this paper, we study the Swendsen-Wang dynamics which is a more sophisticated Mark…
WaveGrad generates high-fidelity audio using gradient estimation.
problem Generating high-fidelity audio efficiently.
method Conditional model using score matching and diffusion models, iteratively refining a Gaussian white noise signal.
result WaveGrad can generate high-fidelity audio samples using as few as six iterations.
Discrete diffusion samplers improve sampling from unnormalised densities.
problem Sampling from discrete unnormalised densities efficiently.
method Introduce off-policy training techniques and data-to-energy Schrödinger bridge training for discrete diffusion samplers.
result Improved performance on synthetic and new benchmarks.
DAIS improves AIS for differentiable marginal likelihood estimation.
problem Differentiable marginal likelihood estimation for complex models.
method Proposes Differentiable Annealed Importance Sampling (DAIS) to make AIS differentiable.
result DAIS achieves convergence and consistency in Bayesian linear regression.
Unified analysis for deterministic samplers in diffusion models.
problem Challenges in analyzing deterministic samplers for diffusion models.
method Unified convergence analysis framework.
result Achieved polynomial iteration complexity for DDIM-type samplers.
Bayesian RL tackles uncertainty with deep generative models and sequential samplers.
problem Optimal decision-making in uncertain environments with limited data.
method Bayesian approach using deep generative models and prequential scoring rule for posterior inference. Policy learning via expected Thompson sampling.
result Improves policy learning in high-dimensional parameter spaces and continuous action spaces.
This paper analyzes MaskGIT sampler and introduces a moment sampler for faster masked diffusion sampling.
problem Efficiently sampling from masked diffusion models.
method Theoretical analysis of MaskGIT sampler, introduction of moment sampler, and two innovations for improving choose-then-sample efficiency.
result The moment sampler is an asymptotically equivalent, more interpretable alternative to MaskGIT.
PTSD improves neural samplers by combining diffusion models and PT, enhancing efficiency.
problem Efficiency and correlation issues in neural samplers compared to PT.
method Sequential training of diffusion models across temperatures, combining high-temperature models for approximate lower-temperature samples.
result Significantly improved target evaluation efficiency, outperforming diffusion-based samplers.
This paper introduces a neural sampler for scalable sampling from complex distributions.
problem Efficiently sampling from high-dimensional un-normalized distributions.
method Neural implicit sampler trained with KL and Fisher divergence methods.
result The neural sampler generates large batches of samples with low computational costs.
Two parallel samplers enhance image quality in limited denoising steps.
problem Limited denoising steps in diffusion models reduce image quality.
method Two parallel samplers denoise at successive times, integrating their information.
result Two parallel samplers improve image quality compared to a single sampler.
For large scale on-line inference problems the update strategy is critical for performance. We derive an adaptive scan Gibbs sampler that optimizes the update frequency by selecting an optimum mini-batch size. We demonstrate performance of our adaptive batch-size Gibbs sampler by comparing it against the collapsed Gibb…
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…
Neural network MCMC sampler maximizes proposal entropy for efficient sampling.
problem Inefficient sampling from complex probability distributions.
method Proposes a neural network MCMC sampler that maximizes proposal entropy.
result Significantly higher efficiency in various sampling tasks.
Develops new bounds for deterministic samplers in diffusion models.
problem Analyzing deterministic samplers in diffusion generative models.
method Operational interpretation of deterministic sampling; restoration and degradation steps.
result First polynomial convergence bounds for DDIM-type samplers.
Gibbs sampling, as a model learning method, is known to produce the most accurate results available in a variety of domains, and is a de facto standard in these domains. Yet, it is also well known that Gibbs random walks usually have bottlenecks, sometimes termed "local maxima", and thus samplers often return suboptima…
PDMP samplers improve Bayesian PDE coefficient inference.
problem Efficient Bayesian inference in non-linear inverse problems with expensive likelihoods.
method Piecewise deterministic Markov process (PDMP) with surrogate-assisted thinning.
result PDMP samplers achieve higher accuracy and efficiency than traditional methods.
The paper evaluates samplers on multi-modal targets, focusing on mode separation and recovery.
problem Handling multi-modality in sampling.
method Synthetic experimental setting focusing on mode relative importance recovery.
result Illustrates the challenges and potential of samplers in multi-modality.
We present a new data-driven benchmark system to evaluate the performance of new MCMC samplers. Taking inspiration from the COCO benchmark in optimization, we view this task as having critical importance to machine learning and statistics given the rate at which new samplers are proposed. The common hand-crafted exampl…
With the rapidly growing scales of statistical problems, subset based communication-free parallel MCMC methods are a promising future for large scale Bayesian analysis. In this article, we propose a new Weierstrass sampler for parallel MCMC based on independent subsets. The new sampler approximates the full data poster…
Unified framework extends adjoint Schrödinger bridge sampler to discrete spaces.
problem Challenges in learning discrete neural samplers due to gradients and combinatorial complexity.
method Introduces discrete ASBS, a unified framework that extends adjoint Schrödinger bridge sampler to discrete spaces.
result Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.
Single-step samplers generate high-quality samples efficiently.
problem Sampling from unnormalized distributions is computationally expensive.
method Developed consistent diffusion samplers that generate samples in a single step.
result Single-step samplers produce high-fidelity samples with less than 1% of traditional samplers' evaluations.
BNEM improves Boltzmann sampler efficiency.
problem Generating IID samples from Boltzmann distributions efficiently.
method Bootstrapped Noised Energy Matching (NEM) combined with diffusion-based learning and bootstrapping.
result BNEM achieves state-of-the-art performance with improved robustness.
LSD distills high-quality samplers for DDMs with fewer steps.
problem Inefficient sampling in DDMs leads to low quality and high computational cost.
method LSD employs a distillation approach to train fast samplers with learnable coefficients and time schedules.
result LSD+ achieves higher sampling quality with fewer steps compared to existing samplers.