Related papers: Asymmetric Matrix-Valued Covariances for Multivari…
This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…
This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
Reliable uncertainty estimates are an important tool for helping autonomous agents or human decision makers understand and leverage predictive models. However, existing approaches to estimating uncertainty largely ignore the possibility of…
We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the…
Covariance functions are a fundamental tool for modeling the dependence structure of spatial processes. This work investigates novel constructions for covariance functions that enable the integration of anisotropies and hole effects in…
This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…
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…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
In this paper, we propose the use of geodesic distances in conjunction with multivariate distance matrix regression, called geometric-MDMR, as a powerful first step analysis method for manifold-valued data. Manifold-valued data is appearing…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
We develop a convex framework for spatially varying coefficient quantile regression that, for each predictor, separates a location-invariant \emph{global} effect from a \emph{spatial deviation}. An adaptive group penalty selects whether a…
This paper presents necessary, sufficient, and equivalent conditions for the spherical convexity of non-homogeneous quadratic functions. In addition to motivating this study and identifying useful criteria for determining whether such…
Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to act as generative models for geometric variation in…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
Circle- and sphere-valued data play a significant role in inverse problems like magnetic resonance phase imaging and radar interferometry, in the analysis of directional information, and in color restoration tasks. In this paper, we aim to…
Space-time covariance modeling under the Lagrangian framework has been especially popular to study atmospheric phenomena in the presence of transport effects, such as prevailing winds or ocean currents, which are incompatible with the…
We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case…
The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…
We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…