Related papers: Zeroth-Order Sampling Methods for Non-Log-Concave …

The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…

Sampling from high-dimensional distributions has wide applications in data science and machine learning but poses significant computational challenges. We introduce Subspace Langevin Monte Carlo (SLMC), a novel and efficient sampling method…

Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…

Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…

The bold diagrammatic Monte Carlo (BDMC) method performs an unbiased sampling of Feynman's diagrammatic series using skeleton diagrams. For lattice models the efficiency of BDMC can be dramatically improved by incorporating dynamic…

Constrained decoding enables Language Models (LMs) to produce samples that provably satisfy hard constraints. However, existing constrained-decoding approaches often distort the underlying model distribution, a limitation that is especially…

We introduce a Markov Chain Monte Carlo (MCMC) method that is designed to sample from target distributions with irregular geometry using an adaptive scheme. In cases where targets exhibit non-Gaussian behaviour, we propose that adaption…

We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on…

This paper presents two novel ensemble domain decomposition methods for fast-solving the Stokes-Darcy coupled models with random hydraulic conductivity and body force. To address such random systems, we employ the Monte Carlo (MC) method to…

In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…

Discrete diffusion models have emerged as powerful frameworks for generating structured categorical data. However, efficiently sampling from reward-tilted distributions remains a fundamental challenge. While Twisted Sequential Monte Carlo…

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…

Fixed-node diffusion Monte Carlo (DMC) is a stochastic algorithm for finding the lowest energy many-fermion wave function with the same nodal surface as a chosen trial function. It has proved itself among the most accurate methods available…

Discrete diffusion language models (dLLMs) provide a fast and flexible alternative to autoregressive models (ARMs) via iterative denoising with parallel updates. However, their evaluation is challenging: existing metrics conflate denoiser…

Diffusion Monte Carlo (DMC) is being recognized as a higher-accuracy, albeit more computationally expensive, alternative to Density Functional Theory (DFT) for energy predictions of catalytic systems. A major computational bottleneck in the…

Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multi-modal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this…

Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Although various studies have explored zeroth-order algorithms,…

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…

This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude.…

In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately…