Related papers: $f$-Divergence Inequalities via Functional Dominat…

We develop a data-driven information-theoretic framework for sharp partial identification of causal effects under unmeasured confounding. Existing approaches often rely on restrictive assumptions, such as bounded or discrete outcomes;…

Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily…

Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…

In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…

Modern applications of conformal inference to multiple testing problems, such as outlier detection and candidate selection, often involve selecting test samples whose conformal p-values fall below a threshold. The quality of such methods is…

The aim of this paper is to study variation detracting property and con- vergence in variation of the Bernstein-Durrmeyer modifications of the classical Bernstein operators in the space of functions of bounded variation. These problems are…

The concept of generalized domination unifies well-known variants of domination-like and independence problems, such as Dominating Set, Independent Set, Perfect Code, etc. A generalized domination (also called $[\sigma,\rho]$-Dominating…

The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…

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…

This paper studies the change point problem for a general parametric, univariate or multivariate family of distributions. An information theoretic procedure is developed which is based on general divergence measures for testing the…

We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…

We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain,…

New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and…

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…

Functional depth is used for ranking functional observations from most outlying to most typical. The ranks produced by functional depth have been proposed as the basis for functional classifiers, rank tests, and data visualization…

We study a natural measurable selection problem for which the standard uniformisation theorems do not seem to apply directly, yet a Borel selector exists. More precisely, we consider families of finite dimensional functions that admit…

The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…

In 2011, Henning, L\"{o}wenstein, and Rautenbach observed that the domination number of a graph is bounded from above by the product of the packing number and the maximum degree of the graph. We prove a stronger statement in subcubic…

Information measures can be constructed from R\'enyi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson $\alpha$-mutual information and has received renewed attention…

This text is based on lectures given by authors in summer 2015. It contains an introduction to the theory of limits over the category of presentations, with examples of different well-known functors like homology or derived functors of…