Related papers: Analysis of the feedback particle filter with diff…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…
This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and…
Feedback particle filters (FPFs) are Monte-Carlo approximations of the solution of the filtering problem in continuous time. The samples or particles evolve according to a feedback control law in order to track the posterior distribution.…
The purpose of this paper is to describe the feedback particle filter algorithm for problems where there are a large number ($M$) of non-interacting agents (targets) with a large number ($M$) of non-agent specific observations…
Despite diffusion models' superior capabilities in modeling complex distributions, there are still non-trivial distributional discrepancies between generated and ground-truth images, which has resulted in several notable problems in image…
This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling…
We introduce a score-based generative sampling method for solving the nonlinear filtering problem with robust accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low stability. To overcome this…
Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…
We derive gain-tuning rules for the positive and negative spatial-feedback loops of a spatially-distributed filter to change the resolution of its spatial band-pass characteristic accordingly to a wavelet zoom, while preserving temporal…
The feedback particle filter (FPF) is a promising nonlinear filtering (NLF) method, but its practical implementation is hindered by the intractability of the gain function, which satisfies a boundary value problem (BVP). This paper proposes…
We establish an algorithm to learn feedback maps from data for a class of robust model predictive control (MPC) problems. The algorithm accounts for the approximation errors due to the learning directly at the synthesis stage, ensuring…
Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…
Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…
A learning approach for optimal feedback gains for nonlinear continuous time control systems is proposed and analysed. The goal is to establish a rigorous framework for computing approximating optimal feedback gains using neural networks.…
Particle filters are applicable to a wide range of nonlinear, non-Gaussian state-space models and have already been applied to a variety of problems. However, there is a problem in the calculation of smoothed distributions, where particles…
The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…