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Sensitivity analysis is an important concept to analyze the influences of parameters in a system, an equation or a collection of data. The methods used for sensitivity analysis are divided into deterministic and statistical techniques.…
In this paper, we investigate the problem of nonparametric monotone frontier estimation from the perspective of extreme value theory. This enables us to revisit the asymptotic theory of the popular free disposal hull estimator in a more…
The effect of measurement errors in discriminant analysis is investigated. Given observations $Z=X+\epsilon$, where $\epsilon$ denotes a random noise, the goal is to predict the density of $X$ among two possible candidates $f$ and $g$. We…
Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods…
We study geometric variations of the discriminating code problem. In the \emph{discrete version} of the problem, a finite set of points $P$ and a finite set of objects $S$ are given in $\mathbb{R}^d$. The objective is to choose a subset…
We show that for any set of $n$ points moving along "simple" trajectories (i.e., each coordinate is described with a polynomial of bounded degree) in $\Re^d$ and any parameter $2 \le k \le n$, one can select a fixed non-empty subset of the…
This paper studies problems of inferring order given noisy information. In these problems there is an unknown order (permutation) $\pi$ on $n$ elements denoted by $1,...,n$. We assume that information is generated in a way correlated with…
Global dynamics in nonlinear stochastic systems is often difficult to analyze rigorously. Yet, many excellent numerical methods exist to approximate these systems. In this work, we propose a method to bridge the gap between computation and…
Assume that $(X_t)_{t\in\Z}$ is a real valued time series admitting a common marginal density $f$ with respect to Lebesgue's measure. Donoho {\it et al.} (1996) propose a near-minimax method based on thresholding wavelets to estimate $f$ on…
We strengthen the Weierstrass approximation theorem by proving that any real-valued continuous function on an interval $I \subset \mathbb{R}$ can be uniformly approximated by a real-valued polynomial whose only (possibly complex) critical…
We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for…
We classify smooth Euler-symmetric varieties corresponding to the symbol system generated by a single reduced polynomial.
We consider the problem of minimal correction of the training set to make it consistent with monotonic constraints. This problem arises during analysis of data sets via techniques that require monotone data. We show that this problem is…
Signal processing in non-Gaussian noise environment is addressed in this paper. For many real-life situations, the additive noise process present in the system is found to be dominantly non-Gaussian. The problem of detection and estimation…
Motivated by problems of uncertainty propagation and robust estimation we are interested in computing a polynomial sublevel set of fixed degree and minimum volume that contains a given semialgebraic set K. At this level of generality this…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
The field of information retrieval often works with limited and noisy data in an attempt to classify documents into subjective categories, e.g., relevance, sentiment and controversy. We typically quantify a notion of agreement to understand…
We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the…
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled…
The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…