Related papers: Approximation of noisy data using multivariate spl…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
This paper presents a novel model-free and fully data-driven policy iteration scheme for quadratic regulation of linear dynamics with state- and input-multiplicative noise. The implementation is similar to the least-squares temporal…
Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…
We propose a bivariate quantile regression method for the bivariate varying coefficient model through a directional approach. The varying coefficients are approximated by the B-spline basis and an $L_{2}$ type penalty is imposed to achieve…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few…
We propose a new method to impute missing values in mixed datasets. It is based on a principal components method, the factorial analysis for mixed data, which balances the influence of all the variables that are continuous and categorical…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
This study introduces an efficient workflow for functional data analysis in classification problems, utilizing advanced orthogonal spline bases. The methodology is based on the flexible Splinets package, featuring a novel spline…
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…
Real world datasets often contain noisy labels, and learning from such datasets using standard classification approaches may not produce the desired performance. In this paper, we propose a Gaussian Mixture Discriminant Analysis (GMDA) with…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
We propose a novel family of multivariate robust smoothers based on the thin-plate (Sobolev) penalty that is particularly suitable for the analysis of spatial data. The proposed family of estimators can be expediently computed even in high…
Penalized spline smoothing is a popular and flexible method of obtaining estimates in nonparametric regression but the classical least-squares criterion is highly susceptible to model deviations and atypical observations. Penalized spline…
A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…