Related papers: Quantile tomography: using quantiles with multivar…
Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…
A new approach to analyzing visual images is proposed, based on the idea of converting an optical image into a spatially varying pattern of polarized squeezed light, which is then used to produce a pattern of chiral edge currents in a thin…
Directional data arise in many applications where observations are naturally represented as unit vectors or as observations on the surface of a unit hypersphere. In this context, statistical depth functions provide a center--outward…
Recent work on depth estimation up to now has only focused on projective images ignoring 360 content which is now increasingly and more easily produced. We show that monocular depth estimation models trained on traditional images produce…
In the present work we have selected a collection of statistical and mathematical tools useful for the exploration of multivariate data and we present them in a form that is meant to be particularly accessible to a classically trained…
Quantile regression permits describing how quantiles of a scalar response variable depend on a set of predictors. Because a unique definition of multivariate quantiles is lacking, extending quantile regression to multivariate responses is…
Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
A comprehensive toolkit is developed for regression analysis of directional data based on a flexible class of angular Gaussian distributions. Informative testing procedures for isotropy and covariate effects on the directional response are…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…
Quantile-based classifiers can classify high-dimensional observations by minimising a discrepancy of an observation to a class based on suitable quantiles of the within-class distributions, corresponding to a unique percentage for all…
The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…
Quantile classifiers for potentially high-dimensional data are defined by classifying an observation according to a sum of appropriately weighted component-wise distances of the components of the observation to the within-class quantiles.…
Deep neural networks are a family of computational models that have led to a dramatical improvement of the state of the art in several domains such as image, voice or text analysis. These methods provide a framework to model complex,…
In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework.…