Related papers: LAMN in a class of parametric models for null recu…

A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest, parameters of common interest to a subset of nodes and parameters of…

We consider non-reversible perturbations of reversible diffusions that do not alter the invariant distribution and we ask whether there exists an optimal perturbation such that the rate of convergence to equilibrium is maximized. We solve…

Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition densities are proved. The observation time [0,T] may be fixed or lim n T = 0, where nh = T and h is a mesh…

Multi-task learning for dense prediction is limited by the need for extensive annotation for every task, though recent works have explored training with partial task labels. Leveraging the generalization power of diffusion models, we extend…

Flood prediction is critical for emergency planning and response to mitigate human and economic losses. Traditional physics-based hydrodynamic models generate high-resolution flood maps using numerical methods requiring fine-grid…

An inductive procedure is developed to calculate the asymptotic behavior at time zero of a diffusion with polynomial drift and degenerate, additive noise. The procedure gives rise to two different rescalings of the process; namely, a…

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…

Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…

We introduce an elementary model of a turbulent boundary layer over a flat surface, given as a vertical random distribution of spanwise Lamb-Oseen vortex configurations placed over a non-slip boundary condition line. We are able to…

Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…

Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…

Pre-trained diffusion models have emerged as powerful generative priors for both unconditional and conditional sample generation, yet their outputs often deviate from the characteristics of user-specific target data. Such mismatches are…

Latent Diffusion models (LDMs) have achieved remarkable results in synthesizing high-resolution images. However, the iterative sampling process is computationally intensive and leads to slow generation. Inspired by Consistency Models (song…

We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…

We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the…

The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. It gives a simplified representation of for example a control…

We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…

Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data…

We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…