Related papers: Approximate Data Depth Revisited
We present a semi-analytic model for the shear two-point correlation function of a cosmic shear survey with non-uniform depth. Ground-based surveys are subject to depth variations that primarily arise through varying atmospheric conditions.…
We consider the linear regression problem of estimating a $p$-dimensional vector $\beta$ from $n$ observations $Y = X \beta + W$, where $\beta_j \stackrel{\text{i.i.d.}}{\sim} \pi$ for a real-valued distribution $\pi$ with zero mean and…
In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- differential equations in a two-dimensional convex polygonal…
In this article, we study approximation properties of the variation spaces corresponding to shallow neural networks with a variety of activation functions. We introduce two main tools for estimating the metric entropy, approximation rates,…
High-dimensional depth separation results for neural networks show that certain functions can be efficiently approximated by two-hidden-layer networks but not by one-hidden-layer ones in high-dimensions $d$. Existing results of this type…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
The purpose of this paper is to introduce two semiparametric methods for the estimation of copula parameter. These methods are based on minimum Alpha-Divergence between a non-parametric estimation of copula density using local likelihood…
We consider low-distortion embeddings for subspaces under \emph{entrywise nonlinear transformations}. In particular we seek embeddings that preserve the norm of all vectors in a space $S = \{y: y = f(x)\text{ for }x \in Z\}$, where $Z$ is a…
We study the derivative-informed learning of nonlinear operators between infinite-dimensional separable Hilbert spaces by neural networks. Such operators can arise from the solution of partial differential equations (PDEs), and are used in…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
In this paper, we introduce Semi-SMD, a novel metric depth estimation framework tailored for surrounding cameras equipment in autonomous driving. In this work, the input data consists of adjacent surrounding frames and camera parameters. We…
Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…
An ultrametric space or infinity-metric space is defined by a dissimilarity function that satisfies a strong triangle inequality in which every side of a triangle is not larger than the larger of the other two. We show that search in…
This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
Semiparametric statistics play a pivotal role in a wide range of domains, including but not limited to missing data, causal inference, and transfer learning, to name a few. In many settings, semiparametric theory leads to (nearly)…
Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying…
Monocular depth estimation has recently progressed beyond ordinal depth to provide metric depth predictions. However, its reliability in underwater environments remains limited due to light attenuation and scattering, color distortion,…
For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…
Accurate, detailed, and regularly updated bathymetry, coupled with complex semantic content, is essential for under-mapped shallow-water environments facing increasing climatological and anthropogenic pressures. However, existing approaches…