Related papers: Minimax nonparametric testing in a problem related…

Given an observation $\mathbf Y \in \mathbb{R}^{d_1\times d_2}$ from the model $\mathbf Y = \mathbf X + \mathbf E$ where $\mathbf X$ is constant and $\mathbf E$ has i.i.d. $N(0,1)$ entries, we consider the problem of detecting a planted…

We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…

High-dimensional classification is a fundamentally important research problem in high-dimensional data analysis. In this paper, we derive a nonasymptotic rate for the minimax excess misclassification risk when feature dimension…

Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…

We study the detection of a change in the covariance matrix of $n$ independent sub-Gaussian random variables of dimension $p$. Our first contribution is to show that $\log\log(8n)$ is the exact minimax testing rate for a change in variance…

Based on discrete observations, we develop a test to infer if the volatility function $\sigma(\cdot)$ within the nonparametric Gaussian white noise model $dY_t = \sigma(t)dW_t$ is constant. The testing procedure is shown to be…

We consider a Gaussian sequence model that contains ill-posed inverse problems as special cases. We assume that the associated operator is partially unknown in the sense that its singular functions are known and the corresponding singular…

We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least…

We consider parameter estimation under sparse linear regression -- an extensively studied problem in high-dimensional statistics and compressed sensing. While the minimax framework has been one of the most fundamental approaches for…

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…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…

In this paper, we consider a class of nonconvex-linear minimax problems on Riemannian manifolds, which find wide applications in machine learning and signal processing. For solving this class of problems, we develop a flexible Riemannian…

We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the null hypothesis states that the regression function $f$…

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…

Many economic parameters are identified by ``thin sets'' (submanifolds with Lebesgue measure zero) and hence difficult to recover from data in an ambient space. This paper provides a unified theory for estimation and inference of such…

We consider non parametric estimation problem for stochastic tomography regression model, i.e. we consider the estimation problem of function of multivariate variables (image) observed through its Radon transformation calculated with the…

We address the problem of adaptive minimax density estimation on $\bR^d$ with $\bL_p$--loss on the anisotropic Nikol'skii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters…

In this review we cover the basics of efficient nonparametric parameter estimation (also called functional estimation), with a focus on parameters that arise in causal inference problems. We review both efficiency bounds (i.e., what is the…

The design of asymptotically minimax robust hypothesis testing is formalized for the Bayesian and Neyman-Pearson tests of Type-I and Type-II. The uncertainty classes based on the KL-divergence, $\alpha$-divergence, symmetrized…