Related papers: Characterizing the Functional Density Power Diverg…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information…
Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density areas and enlarge distances in low density areas. Although…
In this study, we discuss the relationship between two families of density-power-based divergences with functional degrees of freedom -- the H\"{o}lder divergence and the functional density power divergence (FDPD) -- based on their…
Learning about density functional approximations (DFAs), or approximations for the exchange-correlation functional, can be intimidating. Density Functional Theory is now one of the primary simulation tools for the practicing chemist or…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification…
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…
Weak-to-strong generalization (W2SG) has emerged as a promising paradigm for stimulating the capabilities of strong pre-trained models by leveraging supervision from weaker supervisors. To improve the performance of the strong model,…
We examine the equilibrium properties of hot, dilute, non-relativistic plasmas. The partition function and density correlation functions of a classical plasma with several species are expressed in terms of a functional integral over…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
Statistical divergence is widely applied in multimedia processing, basically due to regularity and interpretable features displayed in data. However, in a broader range of data realm, these advantages may no longer be feasible, and…
High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
The logistic loss (a.k.a. cross-entropy loss) is one of the most popular loss functions used for multiclass classification. It is also the loss function of choice for next-token prediction in language modeling. It is associated with the…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
Metrization of statistical divergences is valuable in both theoretical and practical aspects. One approach to obtaining metrics associated with divergences is to consider their fractional powers. Motivated by this idea, Os\'an, Bussandri,…
This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…