Related papers: Correcting Convexity Bias in Function and Function…

Given noisy data, function estimation is considered when the unknown function is known apriori to consist of a small number of regions where the function is either convex or concave. When the regions are known apriori, the estimate is…

Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…

Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators.…

We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function $f$ is observed with additive Gaussian white noise. The function $f$ is assumed to have…

In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…

In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…

Convex regression is a method for estimating the convex function from a data set. This method has played an important role in operations research, economics, machine learning, and many other areas. However, it has been empirically observed…

In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.…

A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…

We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space. Despite the extensive study of function convexity across mathematics, statistics, and computer science, its learnability and…

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…

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…

We extend the problem of obtaining an estimator for the finite population mean parameter incorporating complete auxiliary information through calibration estimation in survey sampling but considering a functional data framework. The…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…

A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…

The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…

We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However,…