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We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
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…
This paper is concerned with forecasting probability density functions. Density functions are nonnegative and have a constrained integral; thus, they do not constitute a vector space. Implementing unconstrained functional time-series…
Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i,…
Bayesian predictive synthesis (BPS) provides a method for combining multiple predictive distributions based on agent/expert opinion analysis theory and encompasses a range of existing density forecast pooling methods. The key ingredient in…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Many models require integrals of high-dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The…
Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces…
The histogram method is a powerful non-parametric approach for estimating the probability density function of a continuous variable. But the construction of a histogram, compared to the parametric approaches, demands a large number of…
Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables,…
Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…
Representing spectral densities, real-frequency, and real-time Green's functions of continuous systems by a small discrete set of complex poles is an ubiquitous problem in condensed matter physics, with applications ranging from quantum…
Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…
In this work we present a new WENO b-spline based quasi-interpolation algorithm. The novelty of this construction resides in the application of the WENO weights to the b-spline functions, that are a partition of unity, instead to the…