Related papers: Optimal minimax random designs for weighted least …
A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…
It is well known that Empirical Risk Minimization (ERM) may attain minimax suboptimal rates in terms of the mean squared error (Birg\'e and Massart, 1993). In this paper, we prove that, under relatively mild assumptions, the suboptimality…
Since its development, the minimax framework has been one of the corner stones of theoretical statistics, and has contributed to the popularity of many well-known estimators, such as the regularized M-estimators for high-dimensional…
In this paper we consider the problem of linear unmixing hidden random variables defined over the simplex with additive Gaussian noise, also known as probabilistic simplex component analysis (PRISM). Previous solutions to tackle this…
In this correspondence, we introduce a minimax regret criteria to the least squares problems with bounded data uncertainties and solve it using semi-definite programming. We investigate a robust minimax least squares approach that minimizes…
In this work, we consider the deterministic optimization using random projections as a statistical estimation problem, where the squared distance between the predictions from the estimator and the true solution is the error metric. In…
We study random designs that minimize the asymptotic variance of a de-biased lasso estimator when a large pool of unlabeled data is available but measuring the corresponding responses is costly. The optimal sampling distribution arises as…
In this article, we investigate the robust optimal design problem for the prediction of response when the fitted regression models are only approximately specified, and observations might be missing completely at random. The intuitive idea…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
We study the problem of causal structure learning over a set of random variables when the experimenter is allowed to perform at most $M$ experiments in a non-adaptive manner. We consider the optimal learning strategy in terms of minimizing…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…
We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…
We study the optimality of the minimax risk of truncated series estimators for symmetric convex polytopes. We show that the optimal truncated series estimator is within $O(\log m)$ factor of the optimal if the polytope is defined by $m$…
In multi-response regression models, the error covariance matrix is never known in practice. Thus, there is a need for optimal designs which are robust against possible misspecification of the error covariance matrix. In this paper, we…
The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in…
I study the minimax-optimal design for a two-arm controlled experiment where conditional mean outcomes may vary in a given set. When this set is permutation symmetric, the optimal design is complete randomization, and using a single…
A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of non-adaptive tomography scales as…