Related papers: On Pairs of $f$-divergences and their Joint Range
Deciding whether the union of two convex polyhedra is itself a convex polyhedron is a basic problem in polyhedral computations; having important applications in the field of constrained control and in the synthesis, analysis, verification…
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…
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…
Given a group G, the conjugacy problem in G is the problem of giving an effective procedure for determining whether or not two given elements f, g of G are conjugate, i.e. whether there exists h belonging to G with fh = hg. This paper is…
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…
We prove the following for a bounded convex planar domain that is symmetric with respect to both coordinate axes. Consider a centered rectangle with sides parallel to the axes that strictly contains the domain. If the domain is not a…
We provide the proof of convergence of the directional diffusion splitting scheme for two-dimensional parabolic and elliptic advection-diffusion-reaction problems with certain restrictions on problem data
We study the problem of estimating the convex hull of the image $f(X)\subset\mathbb{R}^n$ of a compact set $X\subset\mathbb{R}^m$ with smooth boundary through a smooth function $f:\mathbb{R}^m\to\mathbb{R}^n$. Assuming that $f$ is a…
We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in $\mathbb{R}^d$. We prove convergence of the convex hull in the space of all convex and compact subsets of $\mathbb{R}^d$, equipped…
Given an iterated function system of affine dilations with fixed points the vertices of a regular polygon, we characterize which points in the limit set lie on the boundary of its convex hull.
The topic of this paper is related to the well-known notion of unit distance graphs. Take a graph with its edges coloured red and blue such that for some $d$ it can be mapped into the plane with all vertices going to distinct points, the…
In this paper we deal with problems concerning the volume of the convex hull of two "connecting" bodies. After a historical background we collect some results, methods and open problems, respectively.
We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.
In this paper we compute the closure of the numerical range of certain periodic tridiagonal operators. This is achieved by showing that the closure of the numerical range of such operators can be expressed as the closure of the convex hull…
The main result is a direct proof of the implication $(LVKF_{k,3})\Rightarrow( LT_{3k-1,3})$ below. Consider the following statements: ($LVKF_{1,3}$) From any 11 points in $ \mathbb{R}^{3}$ one can choose 3 pairwise disjoint triples whose…
In this paper we have considered a difference of Jensen's inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csisz\'{a}r \cite{csi1} $f-$divergence. A result is established that…
We establish a discrepancy theorem for signed measures, with a given positive part, which are supported on an arbitrary convex curve. As a main application, we obtain a result concerning the distribution of zeros of polynomials orthogonal…
This paper is focused on $f$-divergences, consisting of three main contributions. The first one introduces integral representations of a general $f$-divergence by means of the relative information spectrum. The second part provides a new…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we…