Related papers: Accuracy of Diffusion Approximations for High Freq…
Diffusion processes are widely used for modelling real-world phenomena. Except for select cases however, analytical expressions do not exist for a diffusion process' transitional probabilities. It is proposed that the cumulant truncation…
The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and…
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…
Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
The paper presents efficient approaches for evaluating convergence rate in total variation for finite and general linear Markov chains. The motivation for studying convergence rate in this metric is its usefulness in various limit theorems.…
The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of…
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…
In this paper we propose an adaptive approach for clustering and visualization of data by an orthogonalization process. Starting with the data points being represented by a Markov process using the diffusion map framework, the method…
We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…
Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete…
Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective…
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…
In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We…
This paper uses the generator approach of Stein's method to analyze the gap between steady-state distributions of Markov chains and diffusion processes. Until now, the standard way to invoke Stein's method for this problem was to use the…
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
We show how to calculate individual terms of the Edgeworth series to approximate the distribution of the Pearson correlation coefficient with the help of a simple Mathematica program. We also demonstrate how to eliminate the corresponding…
We discuss sufficient conditions that guarantee the existence of asymptotic expansions for the Central Limit Theorem for weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like…
Finite order Markov models are theoretically well-studied models for dependent discrete data. Despite their generality, application in empirical work when the order is large is rare. Practitioners avoid using higher order Markov models…