Related papers: Spatial-Sign based High-Dimensional Location Test
We consider the problem of deciding whether a highly incomplete signal lies within a given subspace. This problem, Matched Subspace Detection, is a classical, well-studied problem when the signal is completely observed. High- dimensional…
In this paper, we present a new algorithm for semi-supervised representation learning. In this algorithm, we first find a vector representation for the labels of the data points based on their local positions in the space. Then, we map the…
We consider the problem of testing uniformity on high-dimensional unit spheres. We are primarily interested in non-null issues. We show that rotationally symmetric alternatives lead to two Local Asymptotic Normality (LAN) structures. The…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
This paper is concerned with estimation and inference for the location of a change point in the mean of independent high-dimensional data. Our change point location estimator maximizes a new U-statistic based objective function, and its…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
This paper considers a special case of the problem of identifying a static scalar signal, depending on the location, using a planar network of sensors in a distributed fashion. Motivated by the application to monitoring wild-fires spreading…
Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…
This paper considers the problems of detecting a change point and estimating the location in the correlation matrices of a sequence of high-dimensional vectors, where the dimension is large enough to be comparable to the sample size or even…
Although spatial prediction is widely used for urban and environmental monitoring, its accuracy is often unsatisfactory if only a small number of samples are available in the study area. The objective of this study was to improve the…
We consider the problem of change point detection for high-dimensional distributions in a location family when the dimension can be much larger than the sample size. In change point analysis, the widely used cumulative sum (CUSUM)…
Support Vector Machines (SVMs) are popular tools for data mining tasks such as classification, regression, and density estimation. However, original SVM (C-SVM) only considers local information of data points on or over the margin.…
This paper addresses hypothesis testing for the mean of matrix-valued data in high-dimensional settings. We investigate the minimum discrepancy test, originally proposed by Cragg (1997), which serves as a rank test for lower-dimensional…
Sphericity test plays a key role in many statistical problems. We propose Spearman's rho-type rank test and Kendall's tau-type rank test for sphericity in the high dimensional settings. We show that these two tests are equivalent. Thanks to…
We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…
This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general…
Motivated by applications in text mining and discrete distribution inference, we investigate the testing for equality of probability mass functions of $K$ groups of high-dimensional multinomial distributions. A test statistic, which is…
We propose a two-sample mean test based on the Bayes factor with non-informative priors, specifically designed for scenarios where the dimension $p$ grows with the sample size $n$ with a linear rate $p/n \to c_1 \in (0, \infty)$. We…
We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\tilde O(\sqrt{n}\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability…