相关论文: Symmetrization approach to concentration inequalit…

We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…

Variational inequalities are a broad and flexible class of problems that includes minimization, saddle point, and fixed point problems as special cases. Therefore, variational inequalities are used in various applications ranging from…

In the classical two-sample problem, the conventional approach for testing distributions equality is based on the difference between the two marginal empirical distribution functions, whereas a test for independence is based on the contrast…

This paper reconsiders the problem of testing the equality of two unspecified continuous distributions. The framework, which we propose, allows for readable and insightful data visualisation and helps to understand and quantify how two…

A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…

Reaction-diffusion equations are ubiquitous in various scientific domains and their patterns represent a fascinating area of investigation. However, many of these patterns are unstable and therefore challenging to observe. To overcome this…

This paper is concerned with the numerical solution of a class of variational inequalities of the second kind, involving the $p$-Laplacian operator. This kind of problems arise, for instance, in the mathematical modelling of non-Newtonian…

The arithmetic mean/geometric mean-inequality (AM/GM-inequality) facilitates classes of non-negativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic…

We describe a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and thus more easily sampled than their…

We present an efficient parallel derandomization method for randomized algorithms that rely on concentrations such as the Chernoff bound. This settles a classic problem in parallel derandomization, which dates back to the 1980s. Consider…

Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative…

A method for proving symmetrization inequalities for some elliptic p.d.e.'s on manifolds equipped with appropriate isoperimetric inequalities is outlined. The method is based on a modification of an approach of Baernstein. The question of…

Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…

We show that for n>2 the following equivalence problems are essentially the same: the equivalence problem for Lagrangians of order n with one dependent and one independent variable considered up to a contact transformation, a multiplication…

The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…

This paper describes a recent mathematical method called conflation for consolidating data from independent experiments that are designed to measure the same quantity, such as Planck's constant or the mass of the top quark. Conflation is…

This paper studies the convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation. The filtration is general, and the spatial semi-discretization uses the standard continuous piecewise linear…

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…

Following Talagrand's concentration results for permutations picked uniformly at random from a symmetric group [Tal95], Luczak and McDiarmid have generalized it to more general groups G of permutations which act suitably 'locally'. Here we…

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…