Related papers: Function-space regularized R\'enyi divergences
Primal-dual splitting involving proximity operators in order to be able to find some approximation to the minimizer for a general form of Tikhonov type functional is in the focus of this work. This approximation is produced by a pair of…
This paper proposes a unified framework for the investigation of constrained learning theory in reflexive Banach spaces of features via regularized empirical risk minimization. The focus is placed on Tikhonov-like regularization with…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
We present new methods for assessing the privacy guarantees of an algorithm with regard to R\'enyi Differential Privacy. To the best of our knowledge, this work is the first to address this problem in a black-box scenario, where only…
We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…
In R\'enyi's representation for exponential order statistics, we replace the iid exponential sequence with any iid sequence, and call the resulting order statistic generalized R\'enyi statistic. We prove that by randomly reordering the…
Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor…
This work investigates binary hypothesis testing between $H_0\sim P_0$ and $H_1\sim P_1$ in the finite-sample regime under asymmetric error constraints. By employing the ``reverse" R\'enyi divergence, we derive novel non-asymptotic bounds…
A new sharp inequality featuring the differential R\'enyi entropy, the R\'enyi divergence and the R\'enyi cross-entropy of a pair of probability density functions is established. The equality is reached when one of the probability density…
We propose a unified optimization framework for designing continuous and discrete noise distributions that ensure differential privacy (DP) by minimizing R\'enyi DP, a variant of DP, under a cost constraint. R\'enyi DP has the advantage…
In this paper we introduce a biparametric family of transformations which can be seen as an extension of the so-called up and down transformations. This new class of transformations allows to us to introduce new informational functionals,…
This paper studies a specific class of statistical divergences for spectral densities of time series: the spectral $\alpha$-R\'{e}nyi divergences, which include the Itakura-Saito divergence as a limiting case. The aim of this paper is to…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
This paper studies forward and reverse projections for the R\'{e}nyi divergence of order $\alpha \in (0, \infty)$ on $\alpha$-convex sets. The forward projection on such a set is motivated by some works of Tsallis {\em et al.} in…
The asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the…
The aim of this paper is to study different estimation procedures based on $\varphi-$divergences. The dual representation of $\varphi-$divergences based on the Fenchel-Legendre duality is the main interest of this study. It provides a way…
Bregman proximal point algorithm (BPPA) has witnessed emerging machine learning applications, yet its theoretical understanding has been largely unexplored. We study the computational properties of BPPA through learning linear classifiers…
We show that for any $\alpha>0$ the R\'enyi entropy of order $\alpha$ is minimized, among all symmetric log-concave random variables with fixed variance, either for a uniform distribution or for a two sided exponential distribution. The…
R\'enyi divergence is related to R\'enyi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as a measure of information that satisfies almost the same…
This paper is devoted to present new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved…