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Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…
Modelling non-homogeneous and multi-component data is a problem that challenges scientific researchers in several fields. In general, it is not possible to find a simple and closed form probabilistic model to describe such data. That is why…
Radial Basis Function Networks (RBFNs) are used primarily to solve curve-fitting problems and for non-linear system modeling. Several algorithms are known for the approximation of a non-linear curve from a sparse data set by means of RBFNs.…
Mode fitting or "peak-bagging" is an important procedure in helioseismology allowing one to determine the various mode parameters of solar oscillations. We have recently developed a new "pseudo-global" fitting algorithm as a way of reducing…
Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…
The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem…
In this work we report on a new bootstrap method for quantum mechanical problems that closely mirrors the setup from conformal field theory (CFT). We use the equations of motion to develop an analogue of the conformal block expansion for…
Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…
We propose a novel adaptive approximation approach for test-time resource-constrained prediction. Given an input instance at test-time, a gating function identifies a prediction model for the input among a collection of models. Our…
We introduce a semi-parametric Bayesian model for survival analysis. The model is centred on a parametric baseline hazard, and uses a Gaussian process to model variations away from it nonparametrically, as well as dependence on covariates.…
A new method is proposed for fitting non-relativistic binary-scattering data and for extracting the parameters of possible quantum resonances in the compound system that is formed during the collision. The method combines the well-known…
Gaussian processes (GPs) are a mature and widely-used component of the ML toolbox. One of their desirable qualities is automatic hyperparameter selection, which allows for training without user intervention. However, in many realistic…
Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
In this paper the authors study a non-linear elliptic-parabolic system, which is motivated by mathematical models for lithium-ion batteries. One state satisfies a parabolic reaction diffusion equation and the other one an elliptic equation.…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…
We quantify the minimax rate for a nonparametric regression model over a star-shaped function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where…
This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…