Related papers: Upper bounds for the error in some interpolation a…
We consider a finite volume scheme with two-point flux approximation (TPFA) to approximate a Laplace problem when the solution exhibits no more regularity than belonging to $H^1_0(\Omega)$. We establish in this case some error bounds for…
We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
In this paper, we analyze the relative errors in various reliability measures due to the tacit assumption that the components associated with a $n$-component series system or a parallel system are independently working where the components…
This paper studies the possibility of using the survival function to predict long term stability by extrapolation. The survival function is a function of the initial coordinates and is the number of turns a particle will survive for a given…
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the…
A crucial input into causal inference is the imputed counterfactual outcome. Imputation error can arise because of sampling uncertainty from estimating the prediction model using the untreated observations, or from out-of-sample information…
We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by…
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
Let $T_{\epsilon}$ be the noise operator acting on functions on the boolean cube $\{0,1\}^n$. Let $f$ be a nonnegative function on $\{0,1\}^n$ and let $q \ge 1$. We upper bound the $\ell_q$ norm of $T_{\epsilon} f$ by the average $\ell_q$…
In this work, we study the generalization capability of algorithms from an information-theoretic perspective. It has been shown that the expected generalization error of an algorithm is bounded from above by a function of the relative…
This work investigates the stability of (discrete) empirical interpolation for nonlinear model reduction and state field approximation from measurements. Empirical interpolation derives approximations from a few samples (measurements) via…
Machine learning systems, especially with overparameterized deep neural networks, can generalize to novel test instances drawn from the same distribution as the training data. However, they fare poorly when evaluated on out-of-support test…
The aim of this paper is to study the approximation of functions using a higher order Hermite-Fejer interpolation process on the unit circle. The system of nodes is composed of vertically projected zeros of Jacobi polynomials onto the unit…
The maximum utility estimation proposed by Elliott and Lieli (2013) can be viewed as cost-sensitive binary classification; thus, its in-sample overfitting issue is similar to that of perceptron learning. A utility-maximizing prediction rule…
Bayesian parameter estimation provides a systematic approach to compare heavy ion collision models with measurements, leading to constraints on the properties of nuclear matter with proper accounting of experimental and theoretical…
Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed tolerance $\delta$. The lower bound is given on the basis of…
We provide matching upper and lower bounds of order $\sigma^2/\log(d/n)$ for the prediction error of the minimum $\ell_1$-norm interpolator, a.k.a. basis pursuit. Our result is tight up to negligible terms when $d \gg n$, and is the first…