Related papers: Optimization Based Methods for Partially Observed …

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…

Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…

This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational…

We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness…

This work proposes a decision-making framework for partially observable systems in continuous time with discrete state and action spaces. As optimal decision-making becomes intractable for large state spaces we employ approximation methods…

This paper proposes a parallel-in-time method for computing continuous-time maximum-a-posteriori (MAP) trajectory estimates of the states of partially observed stochastic differential equations (SDEs), with the goal of improving…

Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…

We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator…

We present a new method for locating unstable periodic points of one dimensional chaotic maps. This method is based on order statistics. The densities of various maxima of the iterates are discontinuous exactly at unstable periodic points…

The relative degree limitation for adaptive observer-based synchronization schemes is overcome. The scheme is extended to nonpassifiable systems. Two synchronization methods are described and justified based on augmented error adaptive…

Constraining a numerical weather prediction (NWP) model with observations via 4D variational (4D-Var) data assimilation is often difficult to implement in practice due to the need to develop and maintain a software-based tangent linear…

In this review/tutorial article, we present recent progress on optimal control of partially observed Markov Decision Processes (POMDPs). We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where…

The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to…

In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…

This work develops novel strategies for optimal planning with semantic observations using continuous state partially observable markov decision processes (CPOMDPs). Two major innovations are presented in relation to Gaussian mixture (GM)…

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…

An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach…

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…