Related papers: Adaptive Estimation and Uniform Confidence Bands f…
We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to…
Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration…
Supervised machine learning methods require large-scale training datasets to perform well in practice. Synthetic data has been showing great progress recently and has been used as a complement to real data. However, there is yet a great…
In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid. Both the problem of estimating the support function at a point and that of estimating…
In this paper, two types of linear estimators are considered for three related estimation problems involving set-theoretic uncertainty pertaining to $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ balls of frequency-responses. The problems at…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…
We propose a difference-based nonparametric methodology for the estimation and inference of the time-varying auto-covariance functions of a locally stationary time series when it is contaminated by a complex trend with both abrupt and…
Stochastic multi-armed bandits (MABs) provide a fundamental reinforcement learning model to study sequential decision making in uncertain environments. The upper confidence bounds (UCB) algorithm gave birth to the renaissance of bandit…
This paper considers adaptive, minimax estimation of a quadratic functional in a nonparametric instrumental variables (NPIV) model, which is an important problem in optimal estimation of a nonlinear functional of an ill-posed inverse…
When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. To alleviate this linear…
Functional Data Analysis represents a field of growing interest in statistics. Despite several studies have been proposed leading to fundamental results, the problem of obtaining valid and efficient prediction sets has not been thoroughly…
As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set,…
In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is…
We study the adaptive minimax estimation of non-linear integral functionals of a density and extend the results obtained for linear and quadratic functionals to general functionals. The typical rate optimal non-adaptive minimax estimators…
We consider the problem of constructing Bayesian based confidence sets for linear functionals in the inverse Gaussian white noise model. We work with a scale of Gaussian priors indexed by a regularity hyper-parameter and apply the…
Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…
Choice modeling is at the core of understanding how changes to the competitive landscape affect consumer choices and reshape market equilibria. In this paper, we propose a fundamental characterization of choice functions that encompasses a…
This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…