Related papers: Testing zero-dimensionality of varieties at a poin…
This paper adopts a tool from computational topology, the Euler characteristic curve (ECC) of a sample, to perform one- and two-sample goodness of fit tests. We call our procedure TopoTests. The presented tests work for samples of arbitrary…
In this paper, we study Riemannian zeroth-order optimization in settings where the underlying Riemannian metric $g$ is geodesically incomplete, and the goal is to approximate stationary points with respect to this incomplete metric. To…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…
Due to the broad applications of elliptical models, there is a long line of research on goodness-of-fit tests for empirically validating them. However, the existing literature on this topic is generally confined to low-dimensional settings,…
We present an algorithm for computing zero-dimensional tropical varieties based on triangular decomposition and Newton polygon methods. From it, we derive algorithms for computing points on and links of higher-dimensional tropical…
Abelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We investigate here through algebraic methods their consistent deformations ("gaugings"), i.e., the deformations that preserve the number (but…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
We investigate the presence of defects in systems described by real scalar field in (D,1) spacetime dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We…
We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters, and can…
Existing algorithms for isolating real solutions of zero-dimensional polynomial systems do not compute the multiplicities of the solutions. In this paper, we define in a natural way the multiplicity of solutions of zero-dimensional…
We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…
Null shells are a useful geometric construction to study the propagation of infinitesimally thin concentrations of massless particles or impulsive waves. After recalling the necessary and sufficient conditions obtained in [28] that allow…
Sparsity is a basic property of real vectors that is exploited in a wide variety of applications. In this work, we describe property testing algorithms for sparsity that observe a low-dimensional projection of the input. We consider two…
Let X be a d dimensional vector of covariates and Y be the response variable. Under the nonparametric model Y = m(X) + {\sigma}(X) \in we develop an ANOVA-type test for the null hypothesis that a particular coordinate of X has no influence…
In this paper we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a…
Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of given dimension and bounded degree. We call this "testing the…
Efficient recovery of a low-dimensional structure from high-dimensional data has been pursued in various settings including wavelet denoising, generalized linear models and low-rank matrix estimation. By thresholding some parameters to…