Related papers: Exponential contractions and robustness for approx…

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…

This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which…

In many applications, a state-space model depends on a parameter which needs to be inferred from a data set. Quite often, it is necessary to perform the parameter inference online. In the maximum likelihood approach, this can be done using…

This paper considers robust filtering for a nominal Gaussian state-space model, when a relative entropy tolerance is applied to each time increment of a dynamical model. The problem is formulated as a dynamic minimax game where the…

Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

An aperiodic and irreducible Markov chain on a finite state space converges to its stationary distribution. When convergence to equilibrium is measured by total variation distance, there exists an optimal coupling and a maximal coupling…

We propose a new robust filtering paradigm considering the situation in which model uncertainty, described through an ambiguity set, is present only in the observations. We derive the corresponding robust estimator, referred to as…

This article is concerned with the convergence of the state estimate obtained from the discrete time Kalman filter to the continuous time estimate as the temporal discretization is refined. We derive convergence rate estimates for different…

The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to…

This paper develops a robust extended Kalman filter to estimate the rotor angles and the rotor speeds of synchronous generators of a multimachine power system. Using a batch-mode regression form, the filter processes together predicted…

This paper derives recursion equations for a robust smoothing problem for a class of nonlinear systems with uncertainties in modeling and exogenous noise sources. The systems considered operate in discrete-time and the uncertainties are…

We develop a predictive-first optimisation framework for streaming hidden Markov models. Unlike classical approaches that prioritise full posterior recovery under a fully specified generative model, we assume access to regime-specific…

We study robust nonlinear filtering for stochastic models driven by L\'evy processes, where the signal and observation processes are coupled through common Brownian and jump noise. Robustness, defined as the continuous dependence of the…

Using a martingale concentration inequality, concentration bounds `from time $n_0$ on' are derived for stochastic approximation algorithms with contractive maps and both martingale difference and Markov noises. These are applied to…

We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather…

This paper presents a novel algorithm for efficient online estimation of the filter derivatives in general hidden Markov models. The algorithm, which has a linear computational complexity and very limited memory requirements, is furnished…

For additive actuator and sensor faults, we propose a systematic method to design a state-space fault estimation filter directly from Markov parameters identified from fault-free data. We address this problem by parameterizing a…

We introduce a unified framework to estimate the convergence of Markov chains to equilibrium in Wasserstein distance. The framework can provide convergence bounds with rates ranging from polynomial to exponential, all derived from a…

The paper studies the problem of filtering a discrete-time linear system observed by a network of sensors. The sensors share a common communication medium to the estimator and transmission is bit and power budgeted. Under the assumption of…