Related papers: Minimax state estimation for linear continuous dif…
In this paper we present the solution to the problem of optimally discriminating among quantum states, i.e., identifying the states with maximum probability of success when a certain fixed rate of inconclusive answers is allowed. By varying…
We study the fundamental problem of estimating an unknown discrete distribution $p$ over $d$ symbols, given $n$ i.i.d. samples from the distribution. We are interested in minimizing the KL divergence between the true distribution and the…
Kalman filtering is a cornerstone of estimation theory, yet learning the optimal filter under unknown and potentially singular noise covariances remains a fundamental challenge. In this paper, we revisit this problem through the lens of…
Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models…
In this paper, we propose an approach to address the problems with ambiguity in tuning the process and observation noises for a discrete-time linear Kalman filter. Conventional approaches to tuning (e.g. using normalized estimation error…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
Distributed sensor networks often include a multitude of sensors, each measuring parts of a process state space or observing the operations of a system. Communication of measurements between the sensor nodes and estimator(s) cannot…
Minimum divergence problems under integral constraints appear throughout statistics and probability, including sequential inference, bandit theory, and distributionally robust optimization. In many such settings, dual representations are…
We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…
The distributed biased min-consensus (DBMC) protocol is an iterative scheme that solves the shortest path problem asymptotically, requiring only local information exchange between neighboring nodes. By appropriately designing the gain…
This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the…
We deal with the problem of parameter estimation in stochastic differential equations (SDEs) in a partially observed framework. We aim to design a method working for both elliptic and hypoelliptic SDEs, the latters being characterized by…
This paper investigates the state estimation problem for linear systems subject to Gaussian noise, where the model parameters are unknown. By formulating and solving an optimization problem that incorporates both offline and online system…
The scope of this paper is the analysis and approximation of an optimal control problem related to the Allen-Cahn equation. A tracking functional is minimized subject to the Allen-Cahn equation using distributed controls that satisfy…
Structural identification and damage detection can be generalized as the simultaneous estimation of input forces, physical parameters, and dynamical states. Although Kalman-type filters are efficient tools to address this problem, the…
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…
This paper on the whole concerns with the duality of Mayer problem for k-th order differential inclusions, where k is an arbitrary natural number. Thus, this work for constructing the dual problems to differential inclusions of any order…
Prediction error and maximum likelihood methods are powerful tools for identifying linear dynamical systems and, in particular, enable the joint estimation of model parameters and the Kalman filter used for state estimation. A key…
This paper addresses the problem of selecting the minimum number of dedicated sensors to achieve observability in the presence of unknown inputs, namely, the state and input observability, for linear time-invariant systems. We assume that…
General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination…