Related papers: Filtering hidden Markov measures
Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…
We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), a family of non-diffusive stochastic processes consisting of deterministic motion and random jumps at random times. Similarly to…
We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
We propose a joint channel estimation and data detection algorithm for massive multilple-input multiple-output systems based on diffusion models. Our proposed method solves the blind inverse problem by sampling from the joint posterior…
We consider a change detection problem in which the arrival rate of a Poisson process changes suddenly at some unknown and unobservable disorder time. It is assumed that the prior distribution of the disorder time is known. The objective is…
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carr\'e du champ of a Markov process in an abstract space. It leads to a time reversal formula…
Generative models on discrete state-spaces have a wide range of potential applications, particularly in the domain of natural sciences. In continuous state-spaces, controllable and flexible generation of samples with desired properties has…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or…
Employing nonparametric methods for density estimation has become routine in Bayesian statistical practice. Models based on discrete nonparametric priors such as Dirichlet Process Mixture (DPM) models are very attractive choices due to…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
We consider a new type of lookdown processes where spatial motion of each individual is influenced by an individual noise and a common noise, which could be regarded as an environment. Then a class of probability measure-valued processes on…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
Efficiently solving the continuous-time signal and discrete-time observation filtering problem for chaotic dynamical systems presents unique challenges in that the advected distribution between observations may encounter a separatrix…
Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…