Related papers: Efficient Inference in First Passage Time Models

Fastest arrival events, where the first among many diffusing particles reaches a target, are central in triggering signal initiation in molecular stochastic systems. Classical approaches to simulate such events rely on full trajectory…

Denoising diffusion probabilistic models (DDPMs) have recently achieved leading performances in many generative tasks. However, the inherited iterative sampling process costs hindered their applications to speech synthesis. This paper…

We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem…

We develop a generalized method of moments (GMM) approach for fast parameter estimation in a new class of Dirichlet latent variable models with mixed data types. Parameter estimation via GMM has been demonstrated to have computational and…

We study the extremal properties of a stochastic process $x_t$ defined by a Langevin equation $\dot{x}_t=\sqrt{2 D_0 V(B_t)}\,\xi_t$, where $\xi_t$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, and $V(B_t)$ is…

Increasingly, Internet of Things (IoT) domains, such as sensor networks, smart cities, and social networks, generate vast amounts of data. Such data are not only unbounded and rapidly evolving. Rather, the content thereof dynamically…

We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and…

Denoising Diffusion Probabilistic Models (DDPMs) have garnered popularity for data generation across various domains. However, a significant bottleneck is the necessity for whole-network computation during every step of the generative…

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard…

Diffusion probabilistic model (DPM) recently becomes one of the hottest topic in computer vision. Its image generation application such as Imagen, Latent Diffusion Models and Stable Diffusion have shown impressive generation capabilities,…

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…

Denoising diffusion probabilistic models (DDPMs) have achieved impressive performance on various image generation tasks, including image super-resolution. By learning to reverse the process of gradually diffusing the data distribution into…

Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…

In this paper, we first propose an unconditionally stable implicit difference scheme for solving generalized time-space fractional diffusion equations (GTSFDEs) with variable coefficients. The numerical scheme utilizes the $L1$-type formula…

We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Although diffusion models have excelled at capturing data distributions, they still suffer from…

We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…

In cognition, response times and choices in decision-making tasks are commonly modeled using Drift Diffusion Models (DDMs), which describe the accumulation of evidence for a decision as a stochastic process, specifically a Brownian motion,…

This paper introduces an algorithm to select demonstration examples for in-context learning of a query set. Given a set of $n$ examples, how can we quickly select $k$ out of $n$ to best serve as the conditioning for downstream inference?…

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study…