Related papers: Adaptive minimax testing for circular convolution

When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality…

In ill-posed imaging inverse problems, uncertainty quantification remains a fundamental challenge, especially in safety-critical applications. Recently, conformal prediction has been used to quantify the uncertainty that the inverse problem…

We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly expanded the class of applicability of gradient-type methods…

Recently, suboptimality estimates for model predictive controllers (MPC) have been derived for the case without additional stabilizing endpoint constraints or a Lyapunov function type endpoint weight. The proposed methods yield a posteriori…

We consider the non-parametric Poisson regression problem where the integer valued response $Y$ is the realization of a Poisson random variable with parameter $\lambda(X)$. The aim is to estimate the functional parameter $\lambda$ from…

Adaptive optimal control using value iteration initiated from a stabilizing control policy is theoretically analyzed in terms of stability of the system during the learning stage without ignoring the effects of approximation errors. This…

The minimax robust hypothesis testing problem for the case where the nominal probability distributions are subject to both modeling errors and outliers is studied in twofold. First, a robust hypothesis testing scheme based on a relative…

The stochastic block model is widely used for detecting community structures in network data. How to test the goodness-of-fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this article,…

Learning discrete distributions from i.i.d. samples is a well-understood problem. However, advances in generative machine learning prompt an interesting new, non-i.i.d. setting: after receiving a certain number of samples, an estimated…

Goodness-of-fit tests are often used in data analysis to test the agreement of a distribution to a set of data. These tests can be used to detect an unknown signal against a known background or to set limits on a proposed signal…

Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax…

Complete reliance on the fitted model in response surface experiments is risky and relaxing this assumption, whether out of necessity or intentionally, requires an experimenter to account for multiple conflicting objectives. This work…

We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…

In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…

Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…