Related papers: Optimal estimation for regression discontinuity de…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Convex and penalized robust regression methods often suffer from a persistent bias induced by large outliers, limiting their effectiveness in adversarial or heavy-tailed settings. In this work, we study a smooth redescending non-convex…
Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…
This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
In this paper, we consider a finite-dimensional optimization problem minimizing a continuous objective on a compact domain subject to a multi-dimensional constraint function. For the latter, we assume the availability of a global Lipschitz…
We study the least squares regression function estimator over the class of real-valued functions on $[0,1]^d$ that are increasing in each coordinate. For uniformly bounded signals and with a fixed, cubic lattice design, we establish that…
We define "decision swap regret" which generalizes both prediction for downstream swap regret and omniprediction, and give algorithms for obtaining it for arbitrary multi-dimensional Lipschitz loss functions in online adversarial settings.…
This paper proposes the capped least squares regression with an adaptive resistance parameter, hence the name, adaptive capped least squares regression. The key observation is, by taking the resistant parameter to be data dependent, the…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…
This paper considers point and interval estimation of the $\ell_q$ loss of an estimator in high-dimensional linear regression with random design. We establish the minimax rate for estimating the $\ell_{q}$ loss and the minimax expected…
We study regression discontinuity designs in which many predetermined covariates, possibly much more than the number of observations, can be used to increase the precision of treatment effect estimates. We consider a two-step estimator…
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 the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed,…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the…
In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
Experimental designs that are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values.…