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In this paper, we develop a highly parallel and derivative-free fractional neural walk-on-spheres method (FNWoS) for solving high-dimensional fractional Poisson equations on irregular domains. We first propose a simplified fractional…
Diffusion is a fundamental graph procedure and has been a basic building block in a wide range of theoretical and empirical applications such as graph partitioning and semi-supervised learning on graphs. In this paper, we study…
Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first, estimating the score function…
We propose two distributed set-based observers using strip-based and set-propagation approaches for linear discrete-time dynamical systems with bounded modeling and measurement uncertainties. Both algorithms utilize a set-based diffusion…
Personalized retrieval and segmentation aim to locate specific instances within a dataset based on an input image and a short description of the reference instance. While supervised methods are effective, they require extensive labeled data…
A fundamental problem in wireless networks is the \emph{minimum spanning tree} (MST) problem: given a set $V$ of wireless nodes, compute a spanning tree $T$, so that the total cost of $T$ is minimized. In recent years, there has been a lot…
We introduce a new methodology for forecasting which we call Signal Diffusion Mapping. Our approach accommodates features of real world financial data which have been ignored historically in existing forecasting methodologies. Our method…
We propose a robust alignment technique for Standard Fundus Images (SFIs) and Ultra-Widefield Fundus Images (UWFIs), which are challenging to align due to differences in scale, appearance, and the scarcity of distinctive features. Our…
Calculating transition probabilities between different states of multistable climate tipping systems is computationally challenging in high-dimensional models. Targeted algorithms, such as the Trajectory-Adaptive Multilevel Splitting (TAMS)…
Cross-classified data frequently arise in scientific fields such as education, healthcare, and social sciences. A common modeling strategy is to introduce crossed random effects within a regression framework. However, this approach often…
We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational…
This paper brings explicit considerations of distributed computing architectures and data structures into the rigorous design of Sequential Monte Carlo (SMC) methods. A theoretical result established recently by the authors shows that…
This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and $1/t$ algorithms. The classical algorithms are modified by the use of $m$…
Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…
This paper promotes the use of random forests as versatile tools for estimating spatially disaggregated indicators in the presence of small area-specific sample sizes. Small area estimators are predominantly conceptualized within the…
Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
This work describes probabilistic methods for utilizing random spanning trees generated via a random walk process. Goyal et al. showed that the union of random spanning trees approximates the expansion of every cut of a graph. First, we…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
Building on recent advances in scientific machine learning and generative modeling for computational fluid dynamics, we propose a conditional score-based diffusion model designed for multi-scenarios fluid flow prediction. Our model…