Related papers: Delaunay Weighted Two-sample Test for High-dimensi…
So-called linear rank statistics provide a means for distribution-free (even in finite samples), yet highly flexible, two-sample testing in the setting of univariate random variables. Their flexibility derives from a choice of weights that…
We derive the asymptotic distribution of the domination number of a new family of random digraph called proximity catch digraph (PCD), which has application to statistical testing of spatial point patterns and to pattern recognition. The…
We introduce a new statistical quantity the energy to test whether two samples originate from the same distributions. The energy is a simple logarithmic function of the distances of the observations in the variate space. The distribution of…
In this work we introduce a triangular Delaunay mesh generator that can be trained using reinforcement learning to maximize a given mesh quality metric. Our mesh generator consists of a graph neural network that distributes and modifies…
This paper proposes a novel two-step strategy for testing the goodness-of-fit of parametric regression models in ultra-high dimensional sparse settings, where the predictor dimension far exceeds the sample size. This regime usually renders…
We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and…
Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we…
In this paper, we consider the problem of testing independence in high-dimensional settings with missing data. Building upon a recently proposed Kendall-based statistic, we introduce two new modifications specifically designed to…
Two-dimensional Delaunay triangulation is a fundamental aspect of computational geometry. This paper presents a novel algorithm that is specifically designed to ensure the correctness of 2D Delaunay triangulation, namely the Polygonal…
This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using…
Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…
Multi-collinearity is a wide-spread phenomenon in modern statistical applications and when ignored, can negatively impact model selection and statistical inference. Classic tools and measures that were developed for "$n>p$" data are not…
Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…
Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…
Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…
The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that…
We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…
New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented. By illuminating the way these metrics balance density and geometry in the underlying data, we clarify their key parameters and…