Related papers: Variability of qualitative variables: A Hilbert sp…
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…
Ensuring that classifiers are non-discriminatory or fair with respect to a sensitive feature (e.g., race or gender) is a topical problem. Progress in this task requires fixing a definition of fairness, and there have been several proposals…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
Dynamic data selection accelerates training by sampling a changing subset of the dataset while preserving accuracy. We rethink two core notions underlying sample evaluation: representativeness and diversity. Instead of local geometric…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…
Measurement is an integral part of modern science, providing the fundamental means for evaluation, comparison, and prediction. In the context of visualization, several different types of measures have been proposed, ranging from approaches…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
Experimental results presented in this paper supports the hypothesis on quantum-like statistical behaviour of cognitive systems (at least human beings). Our quantum-like approach gives the possibility to represent mental states by Hilbert…
The gradual patterns that model the complex co-variations of attributes of the form "The more/less X, The more/less Y" play a crucial role in many real world applications where the amount of numerical data to manage is important, this is…
Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
This article presents general procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, which are based on quantum probability theory. HSM models can be applied to collections of K different…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
We study de Sitter JT gravity in the canonical formulation to illustrate constructions of Hilbert spaces in quantum gravity, which is challenging due to the Hamiltonian constraints. The key ideas include representing states as "invariants"…
Factors are categorical variables, and the values which these variables assume are called levels. In this paper, we consider the variable selection problem where the set of potential predictors contains both factors and numerical variables.…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
In this paper, a careful treatment of extraction of the Hilbert space and constraints from the formal functional integral with the Einstein-Hilbert action is given. The diffeomorphism inavariant measure is worked out using the metric of…