Related papers: Least-action filtering
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
Consider a diffusion process X=(X_t), with t in [0,1], observed at discrete times and high frequency, solution of a stochastic differential equation whose drift and diffusion coefficients are assumed to be unknown. In this article, we focus…
We propose a large displacement optical flow method that introduces a new strategy to compute a good local minimum of any optical flow energy functional. The method requires a given set of discrete matches, which can be extremely sparse,…
Real-world noise removal is crucial in low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However,…
The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance 54 (1999)…
We propose a new method for the estimation of parameters of hidden diffusion processes. Based on parametrization of the transition matrix, the Baum-Welch algorithm is improved. The algorithm is compared to the particle filter in application…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
We present a new efficient transition pathway search method based on the least action principle and the Gaussian process regression method. Most pathway search methods developed so far rely on string representations, which approximate a…
Out-of-distribution (OOD) detection is a critical task in machine learning that seeks to identify abnormal samples. Traditionally, unsupervised methods utilize a deep generative model for OOD detection. However, such approaches require a…
Consider a reflected diffusion on the positive half-line. We approximate it by solutions of stochastic differential equations using the penalty method: We emulate the "hard barrier" of reflection by a "soft barrier" of a large drift…
Change point detection plays a fundamental role in many real-world applications, where the goal is to analyze and monitor the behaviour of a data stream. In this paper, we study change detection in binary streams. To this end, we use a…
Let $a\in\mathbb{R}$ denote an unknown stationary target with a known distribution $\mu\in\mathcal{P(\mathbb{R}})$, the space of probability measures on $\mathbb{R}$. A diffusive searcher $X(\cdot)$ sets out from the origin to locate the…
In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the…
Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…
This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…