Related papers: On sub-ideal causal smoothing filters
While Dirichlet energy serves as a prevalent metric for quantifying over-smoothing, it is inherently restricted to capturing first-order feature derivatives. To address this limitation, we propose a generalized family of node similarity…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
Particle smoothing enables state estimation in nonlinear and non-Gaussian state-space models, but its practical use is often limited by high computational cost. Backward smoothing methods such as the Forward Filter Backward Smoother (FFBS)…
We consider Kalman filtering problems when the observations are intermittently erased or lost. It was known that the estimates are mean-square unstable when the erasure probability is larger than a certain critical value, and stable…
A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical…
Rule-based models, such as decision trees, appeal to practitioners due to their interpretable nature. However, the learning algorithms that produce such models are often vulnerable to spurious associations and thus, they are not guaranteed…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
In this paper, we develop {finite-time horizon} causal filters using the nonanticipative rate distortion theory. We apply the {developed} theory to {design optimal filters for} time-varying multidimensional Gauss-Markov processes, subject…
A simplified analysis is performed on the Bode-type filtering sensitivity trade-off integrals, which capture the sensitivity characteristics of the estimate and estimation error with respect to the process input and estimated signal in…
Filtering and smoothing with a generalised representation of uncertainty is considered. Here, uncertainty is represented using a class of outer measures. It is shown how this representation of uncertainty can be propagated using…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general…
Machine learning algorithms are designed to capture complex relationships between features. In this context, the high dimensionality of data often results in poor model performance, with the risk of overfitting. Feature selection, the…
It is usual in helioseismology to remove unwanted instrumental low-frequency trends by applying high-pass filters to the time series. However, the choice of the filter is very important because it can keep the periodic signals throughout…
Using a simple thermo-hydrodynamic model that respects relativistic causality, we revisit the analysis of qualitative features of acoustic oscillations in the photon-baryon fluid. The growing photon mean free path introduces transient…
Event-based sampling has been proposed as a general technique for lowering the average communication rate in remote state estimation, which can be important in scenarios with constraints on resources such as network bandwidth or sensor…
This paper is concerned with the large time behavior of solutions to the Euler-Fourier system with damping in $\mathbb{R}^{d}~(d\geq1)$. A time-weighted energy argument has been developed within the $L^2$ framework to derive the optimal…
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…
In this paper, we are interested in obtaining answers to the following questions for particle flow filters: Can we provide a theoretical guarantee that particle flow filters give correct results such as unbiased estimates? Are particle…