Related papers: Joint Range of f-divergences
We compare two f-divergences and prove that their joint range is the convex hull of the joint range for distributions supported on only two points. Some applications of this result are given.
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.
We identify subsets of the joint numerical range of an operator tuple in terms of its joint spectrum. This result helps us to transfer weak convergence of operator orbits into certain approximation and interpolation properties for powers in…
In this technical report we describe some properties of f-divergences and f-GAN training. We present an elementary derivation of the f-divergence lower bounds which form the basis of f-GAN training. We derive informative but perhaps…
In this paper, the concept of the classical $f$-divergence (for a pair of measures) is extended to the mixed $f$-divergence (for multiple pairs of measures). The mixed $f$-divergence provides a way to measure the difference between multiple…
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…
The connection between the commutativity of a family of $n\times n$ matrices and the generalized joint numerical ranges is studied. For instance, it is shown that ${\cal F}$ is a family of mutually commuting normal matrices if and only if…
For a given set of $n\times n$ matrices $\mathcal F$, we study the union of the $C$-numerical ranges of the matrices in the set $\mathcal F$, denoted by $W_C({\mathcal F})$. We obtain basic algebraic and topological properties of…
We present a novel technical method for analyzing the hidden convex structure embedded in the joint range of a quadratic mapping defined on a Hilbert space. Our approach stands out by relying exclusively on elementary mathematical…
A maximum likelihood method is used to deal with the combined estimation of multi-measurements of a branching ratio, where each result can be presented as an upper limit. The joint likelihood function is constructed using observed spectra…
By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate…
Jensen's inequality is ubiquitous in measure and probability theory, statistics, machine learning, information theory and many other areas of mathematics and data science. It states that, for any convex function $f\colon K \to \mathbb{R}$…
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited…
In this paper we discuss the relationship between the numerical range of an extensive class of unbounded operator functions and the joint numerical range of the operator coefficients. Furthermore, we derive methods on how to find estimates…
In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…
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…
In this paper, we propose the Fourier Discrepancy Function, a new discrepancy to compare discrete probability measures. We show that this discrepancy takes into account the geometry of the underlying space. We prove that the Fourier…
The distribution of the number of points of the closed simple random walk, visited a given number of times (the k-multiple point range) is analysed by a graph based approach. A general expression for the moments is derived. In this paper…
We establish various extensions of the convexity Dines theorem for a (joint-range) pair of inhomogeneous quadratic functions. If convexity fails we describe those rays for which the sum of the joint-range and the ray is convex. These…
In this paper, we discuss the joint value distribution of $L$-functions in a suitable class. We obtain joint large deviations results in the central limit theorem for these $L$-functions and some mean value theorems, which give evidence…