Related papers: Quantile tomography: using quantiles with multivar…
As machine learning algorithms are deployed ubiquitously to a variety of domains, it is imperative to make these often black-box models transparent. Several recent works explain black-box models by capturing the most influential features…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
Despite the potential of differentially private data visualization to harmonize data analysis and privacy, research in this area remains underdeveloped. Boxplots are a widely popular visualization used for summarizing a dataset and for…
Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of…
Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…
We propose a M-quantile regression model for the analysis of multivariate, continuous, longitudinal data. M-quantile regression represents an appealing alternative to standard regression models, as it combines the robustness of quantile and…
One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing…
Uncertainty quantification is crucial in time series prediction, and quantile regression offers a valuable mechanism for uncertainty quantification which is useful for extreme value forecasting. Although deep learning models have been…
Estimation of extreme conditional quantiles is often required for risk assessment of natural hazards in climate and geo-environmental sciences and for quantitative risk management in statistical finance, econometrics, and actuarial…
Toroidal microwave cavities are investigated for potential use in quantum information storage and computation. Since exact analytical results are not available for this geometry, extensive numerical simulation has been used to develop a…
The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
Measuring the Data analytically finds the intrinsic manifold in big data. First, Optimal Transport generates the tangent space at each data point from which the intrinsic dimension is revealed. Then, the Koopman Dimensionality Reduction…
The paper presents a versatile library of quasi-analytic complex-valued wavelet packets (WPs) which originate from polynomial splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based orthonormal WPs…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…
Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
Dimensionality reduction is a crucial technique in data analysis, as it allows for the efficient visualization and understanding of high-dimensional datasets. The circular coordinate is one of the topological data analysis techniques…
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…