Related papers: Fast randomized iteration: diffusion Monte Carlo t…

Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…

Random Sample Consensus (RANSAC) is a fundamental approach for robustly estimating parametric models from noisy data. Existing learning-based RANSAC methods utilize deep learning to enhance the robustness of RANSAC against outliers.…

By decomposing the important sampled imaginary time Schr\"odinger evolution operator to fourth order with positive coefficients, we derived a number of distinct fourth order Diffusion Monte Carlo algorithms. These sophisticated algorithms…

The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…

Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…

This work presents self-rewarding sequential Monte Carlo (SMC), an inference-time scaling algorithm enabling effective sampling of masked diffusion language models (MDLMs). Our algorithm stems from the observation that most existing MDLMs…

Employing a classical density-functional description of liquid environments, we introduce a rigorous method for the diffusion quantum Monte Carlo calculation of free energies and thermodynamic averages of solvated systems that requires…

Improving efficiency of importance sampler is at the center of research in Monte Carlo methods. While adaptive approach is usually difficult within the Markov Chain Monte Carlo framework, the counterpart in importance sampling can be…

A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…

This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…

In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its…

In many applications, it is of interest to approximate data, given by mxn matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time…

We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its…

We introduce a Monte Carlo integration-based Shooting and Bouncing Ray (SBR) algorithm for electromagnetic scattering, specifically targeting complex dielectric materials. Unlike traditional deterministic SBR methods, our approach is the…

Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop a novel approach to reduce this…

Consider a central problem in randomized approximation schemes that use a Monte Carlo approach. Given a sequence of independent, identically distributed random variables $X_1,X_2,\ldots$ with mean $\mu$ and standard deviation at most $c…

We propose a neural approach for estimating spatially varying light selection distributions to improve importance sampling in Monte Carlo rendering, particularly for complex scenes with many light sources. Our method uses a neural network…

We present a new algorithm for radiative transfer-based on a statistical Monte Carlo approach-that does not suffer from teleportation effects, on the one hand, and yields smooth results, on the other hand. Implicit Monte Carlo (IMC)…

Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area…