Related papers: Optimal designs for regression with spherical data
Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known…
Minimax designs provide a uniform coverage of a design space $\mathcal{X} \subseteq \mathbb{R}^p$ by minimizing the maximum distance from any point in this space to its nearest design point. Although minimax designs have many useful…
We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…
Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an…
This paper considers the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
Orthogonality constrained optimization is widely used in applications from science and engineering. Due to the nonconvex orthogonality constraints, many numerical algorithms often can hardly achieve the global optimality. We aim at…
The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…
Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary…
Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent…
Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral…
We consider stochastic gradient descent (SGD) for least-squares regression with potentially several passes over the data. While several passes have been widely reported to perform practically better in terms of predictive performance on…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…
We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the…
We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…
For a distribution function $F$ on $\mathbb{R}^d$ and a point $q\in \mathbb{R}^d$, the \emph{spherical depth} $\SphD(q;F)$ is defined to be the probability that a point $q$ is contained inside a random closed hyper-ball obtained from a pair…
Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…