Related papers: Upper bounds for the error in some interpolation a…
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…
The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…
In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the…
Recommendations based on behavioral data may be faced with ambiguous statistical evidence. We consider the case of association rules, relevant e.g.~for query and product recommendations. For example: Suppose that a customer belongs to…
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…
We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…
The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets…
The aim of this paper is to establish various factorization results and then to derive estimates for linear functionals through the use of a generalized Taylor theorem. Additionally, several error bounds are established including…
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…
The problem of optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence ${\zeta}(j)$ from observations of the sequence ${\zeta}(j)+{\theta}(j)$ at points…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
The aim of this paper is to derive a refined first-order expansion formula in Rn, the goal being to get an optimal reduced remainder, compared to the one obtained by usual Taylor's formula. For a given function, the formula we derived is…
Extrapolations of numerical data obtained from finite cluster calculations to the infinite volume limit can often give incorrect results. We discuss four separate cases: (a) the intensity of the lowest two-photon absorption in the infinite…
Practitioners building classifiers often start with a smaller pilot dataset and plan to grow to larger data in the near future. Such projects need a toolkit for extrapolating how much classifier accuracy may improve from a 2x, 10x, or 50x…
We make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation.…
In the era of deep learning, understanding over-fitting phenomenon becomes increasingly important. It is observed that carefully designed deep neural networks achieve small testing error even when the training error is close to zero. One…
We develop an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of…
We determine the pointwise error in Hermite interpolation by numerically solving an appropriate differential equation, derived from the error term itself. We use this knowledge to approximate the error term by means of a polynomial, which…