相关论文: Sup-sums principles for F-divergence, Kullback--Le…

This work presents an infinite-dimensional generalization of the correspondence between the Kullback-Leibler and R\'enyi divergences between Gaussian measures on Euclidean space and the Alpha Log-Determinant divergences between symmetric,…

This paper deals with strong invariance principles (known also as strong approximation theorems) for sums of the form $\sum_{n=1}^{[Nt]}F\big(X(n),X(2n),...,X(kn), X(q_{k+1}(n)),X(q_{k+2}(n)),..., X(q_\ell(n))\big)$

An optimal transport problem on finite spaces is a linear program. Recently, a relaxation of the optimal transport problem via strictly convex functions, especially via the Kullback--Leibler divergence, sheds new light on data sciences.…

In this paper we propose a dimension-reduction strategy in order to improve the performance of importance sampling in high dimension. The idea is to estimate variance terms in a small number of suitably chosen directions. We first prove…

Motivated by the optimality principles for non-subdifferentiable optimization problems, we introduce new relative subdifferentials and examine some properties for relatively lower semicontinuous functions including $\epsilon$-regular…

This paper considers an inexact primal-dual algorithm for semi-infinite programming (SIP) for which it provides general error bounds. To implement the dual variable update, we create a new prox function for nonnegative measures which turns…

Deep learning has been shown to achieve impressive results in several domains like computer vision and natural language processing. A key element of this success has been the development of new loss functions, like the popular cross-entropy…

Inspired by the recent theory of Entropy-Transport problems and by the $\mathbf{D}$-distance of Sturm on normalised metric measure spaces, we define a new class of complete and separable distances between metric measure spaces of possibly…

Derivative based optimization methods are efficient at solving optimal control problems near local optima. However, their ability to converge halts when derivative information vanishes. The inference approach to optimal control does not…

Some inequalities for quantum f-divergence of trace class operators in Hilbert spaces are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum f-divergence in terms of variational and…

We investigate weighted inequalities for fractional maximal operators and fractional integral operators. We work within the innovative framework of "entropy bounds" introduced by Treil--Volberg. Using techniques developed by Lacey and the…

We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple…

We consider nonlinear, or "event-dependent", sampling, i.e. such that the sampling instances {tk} depend on the function being sampled. The use of such sampling in the construction of Lebesgue's integral sums is noted and discussed as…

The Burkhardt--Cottingham sum rule is an exact superconvergence relation for a spin-structure function, derived from general principles of light absorption and scattering, and valid at any momentum transfer $Q^2$. I illustrate how a class…

We consider a family of quantum conditional entropies based on the concept of quantum $f$-divergences. First, we explicitly formulate conditions under which the notion of quantum conditional entropy is well defined in this way. In…

A definition of summability is put forward in the framework of general Carleman ultraholomorphic classes in sectors, so generalizing $k-$summability theory as developed by J.-P. Ramis. Departing from a strongly regular sequence of positive…

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are h-convex and we point out the results for some special…

Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a.…

We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…

A simple method is shown to provide optimal variational bounds on $f$-divergences with possible constraints on relative information extremums. Known results are refined or proved to be optimal as particular cases.