arXiv research

Improved state estimation in high-dimensional models using Zig-Zag Sampler.

Improved PDMP samplers for multi-modal distributions using tempering.

PDMP samplers improve Bayesian PDE coefficient inference.

A new sampler improves the inference of causal structures from observational data.

We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (all scale uniform equivalences). We prove that these equivalences can be characterized with parallel constructions using a combinatoric tool called common zi…

Generative models using PDMPs with explicit jump rates and kernels.

We show that the Khovanov complex of a rational tangle has a very simple representative whose backbone of non-zero morphisms forms a zig-zag. Furthermore, this minimal complex can be computed quickly by an inductive algorithm. (For example, we calculate $Kh(8_2)$ by hand.) We find that the bigradings of the subobjects …

New algorithms solve time-dependent navigation problems, including zig-zag paths.

Corrected samplers reduce discretization error in discrete flow models without additional computational cost.

New samplers improve MCMC efficiency in high dimensions.

New study shows Gaussian samplers struggle with heavy-tailed targets, while stable samplers excel.

SRO optimizes decisions against worst-case sampler induced by generative models.

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…

We construct a zig-zag from the once delooped space of pseudoisotopies of a closed $2n$-disc to the once looped algebraic $K$-theory space of the integers and show that the maps involved are $p$-locally $(2n-4)$-connected for $n>3$ and large primes $p$. The proof uses the computation of the stable homology of the modul…

Discrete diffusion samplers improve sampling from unnormalised densities.

Unified analysis for deterministic samplers in diffusion models.

This paper analyzes MaskGIT sampler and introduces a moment sampler for faster masked diffusion sampling.

PTSD improves neural samplers by combining diffusion models and PT, enhancing efficiency.

This paper introduces a neural sampler for scalable sampling from complex distributions.

Two parallel samplers enhance image quality in limited denoising steps.

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…

New PDMP samplers tackle variable selection in models.

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.

Develops new bounds for deterministic samplers in diffusion models.

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…

The paper evaluates samplers on multi-modal targets, focusing on mode separation and recovery.

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.

Single-step samplers generate high-quality samples efficiently.

BNEM improves Boltzmann sampler efficiency.

LSD distills high-quality samplers for DDMs with fewer steps.

New sampler reduces MCMC complexity for Bayesian variable selection.

Generative neural samplers estimate quantum spin system properties.

Latent Dirichlet Allocation (LDA) is a topic model widely used in natural language processing and machine learning. Most approaches to training the model rely on iterative algorithms, which makes it difficult to run LDA on big corpora that are best analyzed in parallel and distributed computational environments. Indeed…

New sampler tackles complex discrete energy landscapes efficiently.

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…

Improved Gibbs sampler speeds up Bayesian exponential smoothing model.

Bad models can teach well by replicating noise.

Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which \textit{adapt} themselves to obtain better estimators over a sequence of iterations. Although it is straightforward to show that they have the same $\mathcal{O}(1/\sqrt{N})$ convergen…

The pairwise influence matrix of Dobrushin has long been used as an analytical tool to bound the rate of convergence of Gibbs sampling. In this work, we use Dobrushin influence as the basis of a practical tool to certify and efficiently improve the quality of a discrete Gibbs sampler. Our Dobrushin-optimized Gibbs samp…

This work analyzes Gibbs samplers for Bayesian hierarchical models without dimensionality constraints.

Riemannian Proximal Sampler improves sampling on manifold data.

We propose two novel samplers to generate high-quality samples from a given (un-normalized) probability density. Motivated by the success of generative adversarial networks, we construct our samplers using deep neural networks that transform a reference distribution to the target distribution. Training schemes are deve…

New method tunes SMC samplers efficiently without high costs.

Localized sampler tackles high-dimensional sampling with fewer samples.

Adjoint sampler targets infinite-dimensional function spaces for efficient sampling.