Related papers: $f$-Divergence Inequalities via Functional Dominat…
Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…
Let $G=(V,E)$ be a graph. For some $\alpha$ with $0<\alpha \leq 1$, a subset $S$ of $V$ is said to be a $\alpha$-partial dominating set if $|N[S]|\geq \alpha |V|$. The size of a smallest such $S$ is called the $\alpha$-partial domination…
In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…
The barren plateau phenomenon, in which cost-function gradients of variational quantum algorithms vanish exponentially, remains a central obstacle for near-term quantum computing. Existing analyses typically depend on t-design or…
Let $G_1$ and $G_2$ be disjoint copies of a graph $G$, and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…
The domination number $\gamma(G)$ of a graph $G$, its exponential domination number $\gamma_e(G)$, and its porous exponential domination number $\gamma_e^*(G)$ satisfy $\gamma_e^*(G)\leq \gamma_e(G)\leq \gamma(G)$. We contribute results…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…
We explore a family of information measures that stems from R\'enyi's $\alpha$-Divergences with $\alpha<0$. In particular, we extend the definition of Sibson's $\alpha$-Mutual Information to negative values of $\alpha$ and show several…
In the literature, several identification problems in graphs have been studied, of which, the most widely studied are the ones based on dominating sets as a tool of identification. Hereby, the objective is to separate any two vertices of a…
Domain divergence plays a significant role in estimating the performance of a model in new domains. While there is a significant literature on divergence measures, researchers find it hard to choose an appropriate divergence for a given NLP…
This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them.…
In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing the boundedness of a set. The dual principle, although known to the analyst and despite its…
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…
Error bounds are central objects in optimization theory and its applications. They were for a long time restricted only to the theory before becoming over the course of time a field of itself. This paper is devoted to the study of error…
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
We show that under rather general circumstances, the almost everywhere pointwise inequality $|f|(x) \le Mf (x)$ is equivalent to a weak form of the Lebesgue density theorem, for totally bounded closed sets. We derive both positive and…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…