Related papers: Approximate linear minimum variance filters for co…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
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…
The convergence analysis of optimization algorithms using continuous-time dynamical systems has received much attention in recent years. In this paper, we investigate applications of these systems to analyze the convergence of linearized…
The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a…
Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…
The use of non parametric hidden Markov models with finite state space is flourishing in practice while few theoretical guarantees are known in this framework. Here, we study asymptotic guarantees for these models in the Bayesian framework.…
Hidden Markov models (HMMs) are probabilistic functions of finite Markov chains, or, put in other words, state space models with finite state space. In this paper, we examine subspace estimation methods for HMMs whose output lies a finite…
The work is about multiscale stochastic dynamical systems driven by L\'evy processes. First, we prove that these systems can approximate low-dimensional systems on random invariant manifolds. Second, we establish that nonlinear filterings…
Considering the natural ventilation, the thermal behavior of buildings can be described by a linear time varying model. In this paper, we describe an implementation of model reduction of linear time varying systems. We show the consequences…
Relevance vector machine (RVM) can be seen as a probabilistic version of support vector machines which is able to produce sparse solutions by linearly weighting a small number of basis functions instead using all of them. Regardless of a…
We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent…
We consider filtering for a hidden Markov model that evolves with multiple time scales in the hidden states. In particular, we consider the case where one of the states is a scaled Ornstein-Uhlenbeck process with fast reversion to a…
This paper addresses state estimation of linear systems with special attention on unknown process and measurement noise covariances, aiming to enhance estimation accuracy while preserving the stability guarantee of the Kalman filter. To…
Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional…
This article considers the application of particle filtering to continuous-discrete optimal filtering problems, where the system model is a stochastic differential equation, and noisy measurements of the system are obtained at discrete…
This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…
We aim at the construction of a Hidden Markov Model (HMM) of assigned complexity (number of states of the underlying Markov chain) which best approximates, in Kullback-Leibler divergence rate, a given stationary process. We establish, under…
This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…