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We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD). Diffusion maps are used to approximate the generator of the corresponding…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
We present an efficient matrix-free point spread function (PSF) method for approximating operators that have locally supported non-negative integral kernels. The method computes impulse responses at scattered points, and interpolates these…
We present a Bayesian data fusion method to approximate a posterior distribution from an ensemble of particle estimates that only have access to subsets of the data. Our approach relies on approximate probabilistic inference of model…
Nowadays, frequent pattern mining (FPM) on large graphs receives increasing attention, since it is crucial to a variety of applications, e.g., social analysis. Informally, the FPM problem is defined as finding all the patterns in a large…
Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in…
This paper introduces a novel feedback-control based particle filter for the solution of the filtering problem with data association uncertainty. The particle filter is referred to as the joint probabilistic data association-feedback…
The performance of single image super-resolution depends heavily on how to generate and complement high-frequency details to low-resolution images. Recently, diffusion-based DDPM models exhibit great potential in generating high-quality…
The decentralized particle filter (DPF) was proposed recently to increase the level of parallelism of particle filtering. Given a decomposition of the state space into two nested sets of variables, the DPF uses a particle filter to sample…
The particle filter (PF), also known as sequential Monte Carlo (SMC), approximates high-dimensional probability distributions and their normalizing constants in the discrete-time setting. To reduce the variance of the Monte Carlo…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
Graph diffusion models have gained significant attention in graph generation tasks, but they often inherit and amplify topology biases from sensitive attributes (e.g. gender, age, region), leading to unfair synthetic graphs. Existing fair…
In this paper, we revisit the problem of influence maximization with fairness, which aims to select k influential nodes to maximise the spread of information in a network, while ensuring that selected sensitive user attributes are fairly…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled…
The optimal power flow (OPF) is a multi-valued, non-convex mapping from loads to dispatch setpoints. The variability of system parameters (e.g., admittances, topology) further contributes to the multiplicity of dispatch setpoints for a…
We introduce a score-based generative sampling method for solving the nonlinear filtering problem with robust accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low stability. To overcome this…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…