Related papers: Filtering hidden Markov measures
Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where…
Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…
Diffusion models have shown their effectiveness in generation tasks by well-approximating the underlying probability distribution. However, diffusion models are known to suffer from an amplified inherent bias from the training data in terms…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < . . ., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent…
We consider the subdiffusion--absorption process in a system which consists of two different media separated by a thin membrane. The process is described by subdiffusion--absorption equations with fractional Riemann--Liouville time…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…
A Bayesian approach is presented for detecting and characterising the signal from discrete objects embedded in a diffuse background. The approach centres around the evaluation of the posterior distribution for the parameters of the discrete…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…
A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…
Dirichlet process mixtures are particularly sensitive to the value of the precision parameter controlling the behavior of the latent partition. Randomization of the precision through a prior distribution is a common solution, which leads to…
Consider a stationary renewal point process on the real line and divide each of the segments it defines in a proportion given by \iid realisations of a fixed distribution $G$ supported by [0,1]. We ask ourselves for which interpoint…
An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of "piecewise deterministic Markov processes" [Davis], including a broader category of random systems. The corresponding…
Diffusion models generate samples through an iterative denoising process, guided by a neural network. While training the denoiser on real-world data is computationally demanding, the sampling procedure itself is more flexible. This…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity…