Related papers: Optimal Designs for Spherical Harmonic Regression
In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is…
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…
We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…
A finite subset $Y$ on the unit sphere $S^{n-1} \subseteq \mathbb{R}^n$ is called a spherical design of harmonic index $t$, if the following condition is satisfied: $\sum_{\mathbf{x}\in Y}f(\mathbf{x})=0$ for all real homogeneous harmonic…
Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must…
We show how the variational characterisation of spherical designs can be used to take a union of spherical designs to obtain a spherical design of higher order (degree, precision, exactness) with a small number of points. The examples that…
In analogy to classical spherical t-design points, we introduce the concept of t-design curves on the sphere. This means that the line integral along a t-design curve integrates polynomials of degree t exactly. For low degrees we construct…
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…
We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In…
In this short note we propose a new method for construction new nice arrangement on the sphere $S^d$ using the spaces of spherical harmonic.
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…
We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal…
The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation…
This paper is dedicated to the construction of multidimensional spherical monogenics. Firstly, we investigate the construction of monogenic functions in dimension $3$ by applying the Dirac operator to the orthonormal bases of spherical…
This paper studies numerical integration over the unit sphere $ \mathbb{S}^2 \subset \mathbb{R}^{3} $ by using spherical $t$-design, which is an equal positive weights quadrature rule with polynomial precision $t$. We investigate two kinds…
This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class…
For the representation of spin-$s$ band-limited functions on the sphere, we propose a sampling scheme with optimal number of samples equal to the number of degrees of freedom of the function in harmonic space. In comparison to the existing…
The orthonormal set of Spherical Harmonics provides a natural way of expanding whole sky redshift and peculiar velocity surveys.
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…