Related papers: Semi-Parametric Drift and Diffusion Estimation for…
Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…
Diffusion models have shown remarkable performance in generation problems over various domains including images, videos, text, and audio. A practical bottleneck of diffusion models is their sampling speed, due to the repeated evaluation of…
For time-dependent problems with high-contrast multiscale coefficients, the time step size for explicit methods is affected by the magnitude of the coefficient parameter. With a suitable construction of multiscale space, one can achieve a…
We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a…
Weather forecasting remains a crucial yet challenging domain, where recently developed models based on deep learning (DL) have approached the performance of traditional numerical weather prediction (NWP) models. However, these DL models,…
We discuss the effective diffusion constant $D_{{\it eff}}$ for stochastic processes with spatially-dependent noise. Starting from a stochastic process given by a Langevin equation, different drift-diffusion equations can be derived…
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…
We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
In this paper, a practical estimation method for a regression model is proposed using semiparametric efficient score functions applicable to data with various shapes of errors. First, I derive semiparametric efficient score vectors for a…
The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(\cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $k\geq1$, but the…
In this paper we study the properties of the Lasso estimator of the drift component in the diffusion setting. More specifically, we consider a multivariate parametric diffusion model $X$ observed continuously over the interval $[0,T]$ and…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
We study a new parametric approach for hidden discrete-time diffusion models. This method is based on contrast minimization and deconvolution and leads to estimate a large class of stochastic models with nonlinear drift and nonlinear…
This paper presents a communication efficient distributed algorithm, $\mathcal{CIRFE}$ of the \emph{consensus}+\emph{innovations} type, to estimate a high-dimensional parameter in a multi-agent network, in which each agent is interested in…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
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…
Diffusion-based motion planners are becoming popular due to their well-established performance improvements, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…