Related papers: Converting exhausters and coexhausters
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
For a continuous function $f$ defined on a closed and bounded domain, there is at least one maximum and one minimum. First, we introduce some preliminaries which are necessary through the paper. We then present an algorithm, which is…
In this paper the approximation of the optimal compressor function using the first-degree spline functions and quadratic spline functions is done. Coefficients on which we form approximative spline functions are determined by solving…
The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…
Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER,…
An extractor is a function that receives some randomness and either "improves" it or produces "new" randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…
We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
In this article we propose building general-purpose function approximators on top of Haar Scattering Networks. We advocate that this architecture enables a better comprehension of feature extraction, in addition to its implementation…
In minimization models for image recovery and data analysis problems, loss functions and linear operators are typically aggregated as an average of composite terms. Each term in the aggregate models a desired property of the ideal solution…
We derive expressions for the finite-sample distribution of the Lasso estimator in the context of a linear regression model in low as well as in high dimensions by exploiting the structure of the optimization problem defining the estimator.…
Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized…
An extension of Transformers is proposed that enables explicit relational reasoning through a novel module called the Abstractor. At the core of the Abstractor is a variant of attention called relational cross-attention. The approach is…
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem is non-convex when considering standard Barrier and Density methods for invariant sets, and has been treated heuristically by…
For a finite Coxeter group $W$ and $w$ an element of $W$ the `excess' of $w$ is defined to be $e(w) = \min\{\ell(x) + \ell(y) - \ell(w) \; | \; w=xy, \; x^2 = y^2 = 1\}$ where $\ell$ is the length function on $W$. Here we investigate the…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
We present a brief review on the Impulse Approximation method to study processes of scattering off composite particles. We first construct the model in a non-relativistic fashion that enables us to extend the model to a covariant Impulse…
In an effort to develop an alternative approach to traditional sparse reformulations, we will provide a new type of convex reformulation of a large class of stochastic quadratically constrained quadratic optimization problems that is…