Related papers: Filtering in Multivariate Systems with Quantized M…
This work considers the computation of risk measures for quantities of interest governed by PDEs with Gaussian random field parameters using Taylor approximations. While efficient, Taylor approximations are local to the point of expansion,…
We consider the problem of estimating an input signal from noisy measurements in both parallel scalar Gaussian channels and linear mixing systems. The performance of the estimation process is quantified by the $\ell_\infty$ norm error…
An optimal estimator of quantum states based on a modified Kalman's Filter is proposed in this work. Such estimator acts after state measurement, allowing obtain an optimal estimation of quantum state resulting in the output of any quantum…
Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the…
Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…
Most Kalman filter extensions assume Gaussian noise and when the noise is non-Gaussian, usually other types of filters are used. These filters, such as particle filter variants, are computationally more demanding than Kalman type filters.…
Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space…
Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…
We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a…
Gaussian quantum channels constitute a cornerstone of continuous-variable quantum information science, underpinning a wide array of protocols in quantum optics and quantum metrology. While the action of such channels on arbitrary states is…
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…
Sequential Bayesian Filtering aims to estimate the current state distribution of a Hidden Markov Model, given the past observations. The problem is well-known to be intractable for most application domains, except in notable cases such as…
This work presents a novel general regularized distributed solution for the state estimation problem in networked systems. Resting on the graph-based representation of sensor networks and adopting a multivariate least-squares approach, the…
The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the…
Recommender systems are often designed based on a collaborative filtering approach, where user preferences are predicted by modelling interactions between users and items. Many common approaches to solve the collaborative filtering task are…
We first establish a law of large numbers and a convergence theorem in distribution to show the rate of convergence of the non-local means filter for removing Gaussian noise. We then introduce the notion of degree of similarity to measure…
Time-continuous non-anticipating quantum processes of nondemolition measurements are introduced as the dynamical realizations of the causal quasi-measurements, which are described in this paper by the adapted operator-valued probability…
In this paper is proposed a novel incremental iterative Gauss-Newton-Markov-Kalman filter method for state estimation of dynamic models given noisy measurements. The mathematical formulation of the proposed filter is based on the…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…