Related papers: Integral norm discretization and related problems
This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of…
This paper explores the solution of Fredholm-like equations with infinite dimensional solution spaces. We set out to find a method for determining a particular solution to a Fredholm-like equation subject to a given constraint. The…
In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
In this work, we address the problem of polynomial interpolation of non-pointwise data. More specifically, we assume that our input information comes from measurements obtained on diffuse compact domains. Although the nodal and the diffused…
Motivated by many applications, optimal control problems with integer controls have recently received a significant attention. Some state-of-the-art work uses perimeter-regularization to derive stationarity conditions and trust-region…
Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
By discrete trigonometric norming inequalities on subintervals of the period, we construct norming meshes with optimal cardinality growth for algebraic polynomials on sections of sphere, ball and torus.
The many-normal-means problem is a classic example that motivates the development of many important inferential procedures in the history of statistics. In this short note, we consider a further special case of the problem, which involves…
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…
For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative…
This work is devoted to the study of integration with respect to binomial measures. We develop interpolatory quadrature rules and study their properties. Local error estimates for these rules are derived in a general framework.
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
Cosmological fine-tuning has traditionally been associated with the narrowness of the intervals in which the parameters of the physical models must be located to make life possible. A more thorough approach focuses on the probability of the…
We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their…
This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…