Related papers: Proximal Recursion for the Wonham Filter
Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…
We revisit the development of grid based recursive approximate filtering of general Markov processes in discrete time, partially observed in conditionally Gaussian noise. The grid based filters considered rely on two types of state…
We study classes of dynamical systems that can be obtained by constructing recursive networks with monotone Boolean functions. Stack filters in nonlinear signal processing are special cases of such systems. We show an analytical connection…
This paper revisits the question of duality between minimum variance estimation and optimal control first described for the linear Gaussian case in the celebrated paper of Kalman and Bucy. A duality result is established for nonlinear…
We study gradient drift-diffusion processes on a probability simplex set with finite state Wasserstein metrics, namely finite state Wasserstein common noises. A fact is that the Kolmogorov transition equation of finite reversible Markov…
We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…
The Kalman filter is a fundamental filtering algorithm that fuses noisy sensory data, a previous state estimate, and a dynamics model to produce a principled estimate of the current state. It assumes, and is optimal for, linear models and…
Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative…
Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms,…
The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter. However, a fundamental problem in reinforcement learning and control…
We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition…
The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking…
Despite its popularity in the reinforcement learning community, a provably convergent policy gradient method for continuous space-time control problems with nonlinear state dynamics has been elusive. This paper proposes proximal gradient…
Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow for…
The Kalman filter (KF) is one of the most widely used tools for data assimilation and sequential estimation. In this work, we show that the state estimates from the KF in a standard linear dynamical system setting are equivalent to those…
Many applications in aerodynamics, particularly in closed-loop control, depend on sensors to estimate the evolving state of the flow. This estimation task is inherently accompanied by uncertainty due to the noisy measurements of sensors or…
Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that…
Wasserstein gradient flows are continuous time dynamics that define curves of steepest descent to minimize an objective function over the space of probability measures (i.e., the Wasserstein space). This objective is typically a divergence…
We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…
We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a…