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The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…
Under the conventional scale setting, the renormalization scale uncertainty usually constitutes a systematic error for a fixed-order perturbative QCD estimation. The recently suggested principle of maximum conformality (PMC) provides a…
Traditional variable selection methods could fail to be sign consistent when irrepresentable conditions are violated. This is especially critical in high-dimensional settings when the number of predictors exceeds the sample size. In this…
High-dimensional entanglement has been identified as an important resource in quantum information processing, and also as a main obstacle for simulating quantum systems. Its certification is often difficult, and most widely used methods for…
This paper addresses the challenge of classifying polarimetric SAR images by leveraging the peculiar characteristics of the polarimetric covariance matrix (PCM). To this end, a general framework to solve a multiple hypothesis test is…
Not a matter of serious contention, Pearson's correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn't live up to users' needs and expectations.…
The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To simultaneously achieve sparsity and positive…
Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
Conformal prediction, a post-hoc, distribution-free, finite-sample method of uncertainty quantification that offers formal coverage guarantees under the assumption of data exchangeability. Unfortunately, the resulting uncertainty regions…
In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research…
Estimating a covariance matrix and its associated principal components is a fundamental problem in contemporary statistics. While optimal estimation procedures have been developed with well-understood properties, the increasing demand for…
We introduce generalized spatially coupled parallel concatenated codes (GSC-PCCs), a class of spatially coupled turbo-like codes obtained by coupling parallel concatenated codes (PCCs) with a fraction of information bits repeated before the…
In the field of unsupervised feature selection, sparse principal component analysis (SPCA) methods have attracted more and more attention recently. Compared to spectral-based methods, SPCA methods don't rely on the construction of a…
This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an $m$-by-$n$ nonnegative matrix $X$ and an integer $k$, the PSD factorization…
Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
In applied multivariate statistics, estimating the number of latent dimensions or the number of clusters, $k$, is a fundamental and recurring problem. We study a sequence of statistics called "cross-validated eigenvalues." Under a large…
Conformal prediction is a popular technique for constructing prediction intervals with distribution-free coverage guarantees. The coverage is marginal, meaning it only holds on average over the entire population but not necessarily for any…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…