Related papers: Approximate Data Depth Revisited

Given a Hilbert space $\mathcal H$ and a finite measure space $\Omega$, the approximation of a vector-valued function $f: \Omega \to \mathcal H$ by a $k$-dimensional subspace $\mathcal U \subset \mathcal H$ plays an important role in…

We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality. For metric spaces, the doubling dimension…

Let $P$ be a set of $n$ points in $d$-dimensions. The simplicial depth, $\sigma_P(q)$ of a point $q$ is the number of $d$-simplices with vertices in $P$ that contain $q$ in their convex hulls. The simplicial depth is a notion of data depth…

Without ground truth supervision, self-supervised depth estimation can be trapped in a local minimum due to the gradient-locality issue of the photometric loss. In this paper, we present a framework to enhance depth by leveraging semantic…

We study function estimation in the empirical Bayes setting for Poisson and normal means. Specifically, given observations $Y_i\sim f(\cdot; \theta_i)$ with latent parameters $\theta_i\sim \pi$, the goal is to estimate…

Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To…

We consider the problem of approximating a semialgebraic set with a sublevel-set of a polynomial function. In this setting, it is standard to seek a minimum volume outer approximation and/or maximum volume inner approximation. As there is…

A fully analytical description of the allowed $\beta$ spectrum shape is given in view of ongoing and planned measurements. Its study forms an invaluable tool in the search for physics beyond the standard electroweak model and the weak…

Data depth has emerged as an invaluable nonparametric measure for the ranking of multivariate samples. The main contribution of depth-based two-sample comparisons is the introduction of the Q statistic (Liu and Singh, 1993), a quality…

The sensitivity of all-sky searches for gravitational-wave pulsars is primarily limited by the finite availability of computing resources. Semicoherent searches are a widely-used method of maximizing sensitivity to gravitational-wave…

One-dimensional function approximation is a fundamental problem in scientific computing and engineering applications. While neural networks possess powerful universal approximation capabilities, their optimization process is often hindered…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

In this article we introduce a notion of depth functions for data types that are not given in standard statistical data formats. We focus on data that cannot be represented by one specific data structure, such as normed vector spaces. This…

With the ubiquity of sensors in the IoT era, statistical observations are becoming increasingly available in the form of massive (multivariate) time-series. Formulated as unsupervised anomaly detection tasks, an abundance of applications…

This paper introduces and studies multivariate spacings. The spacings are developed using the order statistics derived from data depth. Specifically, the spacing between two consecutive order statistics is the region which bridges the two…

We propose a novel data-driven approach for high-resolution bathymetric reconstruction from sidescan. Sidescan sonar (SSS) intensities as a function of range do contain some information about the slope of the seabed. However, that…

The level set estimation problem seeks to find all points in a domain ${\cal X}$ where the value of an unknown function $f:{\cal X}\rightarrow \mathbb{R}$ exceeds a threshold $\alpha$. The estimation is based on noisy function evaluations…

In this article, we propose a novel discretization method based on numerical integration for discretizing continuous systems, termed the $\alpha\beta$-approximation or Scalable Bilinear Transformation (SBT). In contrast to existing methods,…

Most existing methods often rely on complex models to predict scene depth with high accuracy, resulting in slow inference that is not conducive to deployment. To better balance precision and speed, we first designed SmallDepth based on…

We give the first differentially private algorithms that estimate a variety of geometric features of points in the Euclidean space, such as diameter, width, volume of convex hull, min-bounding box, min-enclosing ball etc. Our work relies…