Related papers: Variability of qualitative variables: A Hilbert sp…
This study investigates the extension of distance variance, a validated spread metric for continuous and binary variables [Edelmann et al., 2020, Ann. Stat., 48(6)], to quantify the spread of general categorical variables. We provide both…
We discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in…
This paper explores the problem of uncertainty quantification in the behavioral setting for data-driven control. Building on classical ideas from robust control, the problem is regarded as that of selecting a metric which is best suited to…
When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that…
This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. We solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
In each of the last five years, a few dozen empirical studies appeared in visualization journals and conferences. The existing empirical studies have already featured a large number of variables. There are many more variables yet to be…
Correlation and similarity measures are widely used in all the areas of sciences and social sciences. Often the variables are not numbers but are instead qualitative descriptors called categorical data. We define and study similarity…
This article considers linear processes with values in a separable Hilbert space exhibiting long-range dependence. The scaling limits for the sample autocovariance operators at different time lags are investigated in the topology of their…
We develop a framework for regularly varying measures on complete separable metric spaces $\mathbb{S}$ with a closed cone $\mathbb{C}$ removed, extending material in Hult & Lindskog (2006), Das, Mitra & Resnick (2013). Our framework…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
There is presented a contextual statistical model of the probabilistic description of physical reality. Here contexts (complexes of physical conditions) are considered as basic elements of reality. There is discussed the relation with QM.…
The problem of efficiently training and evaluating image classifiers that can distinguish between a large number of object categories is considered. A novel metric, sharpness, is proposed which is defined as the fraction of object…
Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…
One considers Hilbert space valued measures on the Borel sets of a compact metric space. A natural numerical valued integral of vector valued continuous functions with respect to vector valued functions is defined. Using this integral,…
We introduce a new formulation for differential equation describing dynamics of measures on an Euclidean space, that we call Measure Differential Equations with sources. They mix two different phenomena: on one side, a transport-type term,…
In this paper, we construct new multifractal measures, on the Euclidean space $\mathbb{R}^n$, in a similar manner to Hewitt-Stomberg measures but using the class of all $n$-dimensional half-open binary cubes of covering sets in the…
In a previous paper, we presented an Abstract Beurling's Theorem for valuation Hilbert modules over valuation algebras. In this paper, we shall apply this theorem to obtain complete descriptions of the closed invariant subspaces of a number…
While variable selection has received extensive attention in the literature, its exploration in the presence of response measurement error remains underexplored. In this paper, we investigate this important problem within the context of…
An algebraic structure underlying the quantity calculus is proposed consisting in an algebraic fiber bundle, that is, a base structure which is a free Abelian group together with fibers which are one dimensional vector spaces, all of them…