相关论文: Exact simulation of diffusions

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…

Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…

We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…

Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality significantly, but have posed challenges to find the exact inverse (i.e., finding the…

We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling…

This paper is concerned with differentiable resampling in the context of sequential Monte Carlo (e.g., particle filtering). Drawing on reparametrisation, we propose a new resampling method that is informative and instantly differentiable,…

This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and…

We present a new random walk for uniformly sampling high-dimensional convex bodies. It achieves state-of-the-art runtime complexity with stronger guarantees on the output than previously known, namely in R\'enyi divergence (which implies…

We introduce a novel, training-free method for sampling differentiable representations (diffreps) using pretrained diffusion models. Rather than merely mode-seeking, our method achieves sampling by "pulling back" the dynamics of the…

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…

We introduce a path sampling method for the computation of rate constants for systems with a highly diffusive character. Based on the recently developed algorithm of transition interface sampling (TIS) this procedure increases the…

A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is…

In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground…

The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or…

An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to…

We set up a real-time path integral to study the evolution of quantum systems driven in real-time completely by the coupling of the system to the environment. For specifically chosen interactions, this can be interpreted as measurements…

The first-passage time is a key concept in stochastic modeling, representing the time at which a process first reaches a specified threshold. In this work, we consider a jump-diffusion (JD) model with a time-dependent threshold, providing a…

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…

We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…