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This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into…
Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…
Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most CP methods focus on building…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in…
Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…
We study the complexity of approximating the permanent of a positive semidefinite matrix $A\in \mathbb{C}^{n\times n}$. 1. We design a new approximation algorithm for $\mathrm{per}(A)$ with approximation ratio $e^{(0.9999 + \gamma)n}$,…
We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…
Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…
A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale $\mu_R$ and thus determining the correct values of the QCD running coupling $\alpha_s(\mu_R^2)$ at each order in the perturbative…
Cosmological parameter estimation requires that the likelihood function of the data is accurately known. Assuming that cosmological large-scale structure power spectra data are multivariate Gaussian-distributed, we show the accuracy of…
System-on-Chip (SoC) designs are used in every aspect of computing and their optimization is a difficult but essential task in today's competitive market. Data taken from SoCs to achieve this is often characterised by very long concurrent…
Identifying multivariate dependencies in high-dimensional data is an important problem in large-scale inference. This problem has motivated recent advances in mining (partial) correlations, which focus on the challenging ultra-high…
When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the…
I present the Phase Distance Correlation (PDC) periodogram -- a new periodicity metric, based on the Distance Correlation concept of G\'abor Sz\'ekely. For each trial period PDC calculates the distance correlation between the data samples…
A new class of spatially-coupled turbo-like codes (SC-TCs), dubbed generalized spatially coupled parallel concatenated codes (GSC-PCCs), is introduced. These codes are constructed by applying spatial coupling on parallel concatenated codes…
Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…