Reduced-order models for linear time-invariant dynamical systems are considered and the error between the full-order model and the reduced-order model solutions is characterized. Based on the analytical representation of the error, an a posteriori error indicator is proposed that combines a Krylov-based exponential integrator and an a posteriori residual-based estimate. Numerical experiments il...

We present a new method for obtaining confidence intervals in steady-state simulation. In our replicated batch means method, we do a small number of independent replications to estimate the steady-state mean of the underlying stochastic process. In order to obtain a variance estimator, we further group the observations from these replications into nonoverlapping batches. We show that for large ...

The kernel-based regularization method has two core issues: kernel design and hyperparameter estimation. In this paper, we focus on the second issue and study the properties of several hyperparameter estimators including the empirical Bayes (EB) estimator, two Stein’s unbiased risk estimators (SURE) and their corresponding Oracle counterparts, with an emphasis on the asymptotic properties of th...

In one-bit compressed sensing (1-bit CS), one attempts to estimate a structured parameter (signal) only using the sign of suitable linear measurements. In this paper, we investigate 1-bit CS problems for sparse signals using the recently proposed k-support norm. We show that the new estimator has a closed-form solution, so no optimization is needed. We establish consistency and recovery guarant...

I consider the estimation of linear regression models when the independent variables are measured with errors whose variances differ across observations, a situation that arises, for example, when the explanatory variables in a regression model are estimates of population parameters based on samples of varying sizes. Replacing the error variance that is assumed common to all observations in the...

In this paper, we propose a new formulation of the classical Good-Turing estimator for -gram language model. The new approach is based on defining a dynamic model for language production. Instead of assuming a fixed probability distribution of occurrence of an -gram on the whole text, we propose a maximum entropy approximation of a time varying distribution. This approximation led us to a new d...

This paper studies time-inhomogeneous diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production for a process with respect to transient invariant probability measures. also study time reversal reverse in Crooks’s fluctuation theorem. show that coincides optimally controlled forward leads zero variance importance sampli...

This paper deals with fault detection and more particularly with the Fundamental Problem of Residual Generation (FPRG). In former works, conditions, based on the properties of invariant distributions involving the disturbance vector field, were given to solve this problem. The aim of the present paper is to provide, when those conditions are not fulfilled, an alternative solution to the FPRG, b...