Related papers: In-and-Out: Algorithmic Diffusion for Sampling Con…
We prove an exponential deviation inequality for the convex hull of a finite sample of i.i.d. random points with a density supported on an arbitrary convex body in $\R^d$, $d\geq 2$. When the density is uniform, our result yields rate…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near…
We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration…
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
We consider random instances of non-convex perceptron problems in the high-dimensional limit of a large number of examples $M$ and weights $N$, with finite load $\alpha = M/N$. We develop a formalism based on replica theory to predict the…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…
We give a polynomial-time algorithm for learning high-dimensional halfspaces with margins in $d$-dimensional space to within desired TV distance when the ambient distribution is an unknown affine transformation of the $d$-fold product of an…
Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
This work develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II to have a wider stability range…
We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential…
Diffusion models have become a leading method for generative modeling of both image and scientific data. As these models are costly to train and \emph{evaluate}, reducing the inference cost for diffusion models remains a major goal.…
We develop a short-step interior point method to optimize a linear function over a convex body assuming that one only knows a membership oracle for this body. The approach is based on Abernethy and Hazan's sketch of a universal interior…
The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully…
Traditionally, time-development of the mean square displacement has been employed to determine the diffusion coefficient from the trajectories of single particles. However, this approach is sensitive to the noise and the motion blur upon…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
We present a mechanism to steer the sampling diversity of denoising diffusion and flow matching models, allowing users to sample from a sharper or broader distribution than the training distribution. We build on the observation that these…
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…