Related papers: Optimal designs for rational function regression
Consider an experiment with a finite set of design points representing permissible trial conditions. Suppose that each trial is associated with a cost that depends on the selected design point. In this paper, we study the problem of…
We study $L_p$ polynomial regression. Given query access to a function $f:[-1,1] \rightarrow \mathbb{R}$, the goal is to find a degree $d$ polynomial $\hat{q}$ such that, for a given parameter $\varepsilon > 0$, $$ \|\hat{q}-f\|_p\le…
Tie-breaker designs trade off a statistical design objective with short-term gain from preferentially assigning a binary treatment to those with high values of a running variable $x$. The design objective is any continuous function of the…
The celebrated de la Garza phenomenon states that for a polynomial regression model of degree $p-1$ any optimal design can be based on at most $p$ design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499--2524] showed that…
D-Optimal designs for estimating parameters of response models are derived by maximizing the determinant of the Fisher information matrix. For non-linear models, the Fisher information matrix depends on the unknown parameter vector of…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
One of the desirable objectives in feedback control design is to formulate and solve the design problem as an optimisation problem that is convex, so that an optimal solution can be found efficiently. Unfortunately many control design…
In this paper we investigate the possibility of obtaining a measure representation for function- als arising in the context of optimal design problems under non-standard growth conditions and perimeter penalization. Applications to…
This paper presents the benefits of using randomized neural networks instead of standard basis functions or deep neural networks to approximate the solutions of optimal stopping problems. The key idea is to use neural networks, where the…
We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…
We consider a general $p$-norm objective for experimental design problems that captures some well-studied objectives (D/A/E-design) as special cases. We prove that a randomized local search approach provides a unified algorithm to solve…
We characterize $D$-optimal designs in the two-dimensional Poisson regression model with synergetic interaction and provide an explicit proof. The proof is based on the idea of reparameterization of the design region in terms of contours of…
The Regression Discontinuity (RD) design is one of the most widely used non-experimental methods for causal inference and program evaluation. Over the last two decades, statistical and econometric methods for RD analysis have expanded and…
We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving…
Uncertainties such as manufacturing tolerances cause performance variations in complex engineering systems, making robust design optimization (RDO) essential. However, simulation-based RDO faces high computational cost for statistical…
Two-phase designs measure variables of interest on a subcohort where the outcome and covariates are readily available or cheap to collect on all individuals in the cohort. Given limited resource availability, it is of interest to find an…
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…
Optimal experimental design is an essential subfield of statistics that maximizes the chances of experimental success. The D- and A-optimal design is a very challenging problem in the field of optimal design, namely minimizing the…
It is often desired that ordinal regression models yield unimodal predictions. However, in many recent works this characteristic is either absent, or implemented using soft targets, which do not guarantee unimodal outputs at inference. In…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…