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Related papers: A Note on Reverse Pinsker Inequalities

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The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is…

Analysis of PDEs · Mathematics 2014-01-03 Sebastian Acosta , Sum Chow , James Taylor , Vianey Villamizar

Given a pair of predictor variables and a response variable, how much information do the predictors have about the response, and how is this information distributed between unique, redundant, and synergistic components? Recent work has…

Information Theory · Computer Science 2018-10-29 Pradeep Kr. Banerjee , Johannes Rauh , Guido Montúfar

We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…

Computer Vision and Pattern Recognition · Computer Science 2011-12-06 Jan Lellmann , Frank Lenzen , Christoph Schnörr

The Pinsker inequality lower bounds the Kullback--Leibler divergence $D_{\textrm{KL}}$ in terms of total variation and provides a canonical way to convert $D_{\textrm{KL}}$ control into $\lVert \cdot \rVert_1$-control. Motivated by…

Information Theory · Computer Science 2026-02-06 Guglielmo Beretta , Tommaso Cesari , Roberto Colomboni

Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…

Optimization and Control · Mathematics 2020-08-05 Vincent Duval

In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…

Optimization and Control · Mathematics 2026-01-27 Pavel Dvurechensky , Meggie Marschner , Shimrit Shtern , Mathias Staudigl

Exact lower and upper bounds on the best possible misclassification probability for a finite number of classes are obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. These…

Statistics Theory · Mathematics 2018-02-12 Iosif Pinelis

This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…

Probability · Mathematics 2019-11-19 Paul Dupuis , Yixiang Mao

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…

Methodology · Statistics 2024-09-05 Luca Maestrini , Robert G. Aykroyd , Matt P. Wand

This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…

Optimization and Control · Mathematics 2014-05-19 Shakoor Pooseh , Ricardo Almeida , Delfim F. M. Torres

The authors found extremals of arbitrary left-invariant sub-Finsler metric on the Engel group defined by a distribution of rank two. They use for this the Pontryagin Maximum Principle for the corresponding time-optimal problem in…

Differential Geometry · Mathematics 2020-06-12 Valera Berestovskii , Irina Zubareva

This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…

Numerical Analysis · Mathematics 2021-11-23 Toni Sayah

We give a simple inequality for the sum of independent bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.

Probability · Mathematics 2012-10-25 Christopher R. Dance

The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…

Data Analysis, Statistics and Probability · Physics 2007-09-19 S. Yellin

Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…

Probability · Mathematics 2024-08-30 Celine Moucer , Adrien Taylor , Francis Bach

Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…

Optimization and Control · Mathematics 2019-07-19 Timothy C. Y. Chan , Neal Kaw

This paper proposes a partially inexact alternating direction method of multipliers for computing approximate solution of a linearly constrained convex optimization problem. This method allows its first subproblem to be solved inexactly…

Optimization and Control · Mathematics 2018-05-21 Vando A. Adona , Max L. N. Goncalves , Jefferson G. Melo

Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…

In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…

Probability · Mathematics 2026-04-10 Fraser Daly

We present here a variational method for maximizing the bandgap in a one-dimensional system where the potential is subject to given constraints. Two specific examples are studied in detail. In the first, we show that if the potential is…

Mathematical Physics · Physics 2007-05-23 Prabasaj Paul , Bill Sutherland
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