Related papers: In-and-Out: Algorithmic Diffusion for Sampling Con…
We study nonconvex distributed optimization in multiagent networks where the communications between nodes is modeled as a time-varying sequence of arbitrary digraphs. We introduce a novel broadcast-based distributed algorithmic framework…
Most motion deblurring algorithms rely on spatial-domain convolution models, which struggle with the complex, non-linear blur arising from camera shake and object motion. In contrast, we propose a novel single-image deblurring approach that…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
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…
Hit-and-Run is known to be one of the best random sampling algorithms, its mixing time is polynomial in dimension. Nevertheless, in practice the number of steps required to achieve uniformly distributed samples is rather high. We propose…
We examine the Langevin diffusion confined to a closed, convex domain $D\subset\mathbb{R}^d$, represented as a reflected stochastic differential equation. We introduce a sequence of penalized stochastic differential equations and prove that…
In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
This paper presents a novel method designed to enhance the efficiency and accuracy of both image retrieval and pixel retrieval. Traditional diffusion methods struggle to propagate spatial information effectively in conventional graphs due…
Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…
We study strongly convex distributed optimization problems where a set of agents are interested in solving a separable optimization problem collaboratively. In this paper, we propose and study a two time-scale decentralized gradient descent…
A global picture of a random particle movement is given by the convex hull of the visited points. We obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…
We show how to sample in parallel from a distribution $\pi$ over $\mathbb R^d$ that satisfies a log-Sobolev inequality and has a smooth log-density, by parallelizing the Langevin (resp. underdamped Langevin) algorithms. We show that our…
We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of integration is…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…