Related papers: The Bernstein-Orlicz norm and deviation inequaliti…
We introduce a new operational technique for deriving chain rules for general information theoretic quantities. This technique is very different from the popular (and in some cases fairly involved) methods like SDP formulation and operator…
The aim of this paper is investigating of Orlicz spaces with exponential function and correspondence Orlicz norm: we introduce some new equivalent norms, obtain the tail characterization, study the product of functions in Orlicz spaces etc.…
We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm.…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
In this paper we study the regularity of paths in terms of properties of admissible nets. We show the right concentration inequality above the modulus of continuity. Using the approach we prove the Bernstein type inequality for the…
The first part of this work considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
In the regression framework, the empirical measure based on the responses resulting from the nearest neighbors, among the covariates, to a given point $x$ is introduced and studied as a central statistical quantity. First, the associated…
A new Berry-Esseen bound for non-linear functionals of non-symmetric and non-homogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein method and an analysis of the discrete…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…
We introduce a new type of estimator for the spectral tail process of a regularly varying time series. The approach is based on a characterizing invariance property of the spectral tail process, which is incorporated into the new estimator…
We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
In this paper, we develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of…
We introduce a nonasymptotic framework for sub-Poisson distributions with moment generating function dominated by that of a Poisson distribution. At its core is a new notion of optimal sub-Poisson variance proxy, analogous to the variance…
We obtain the tail probability of generalized sub-Gaussian canonical processes. It can be viewed as a variant of the Bernstein-type inequality in the i.i.d case, and we further get a tighter bound of concentration inequality through…
In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…