Related papers: Minimax experimental design: Bridging the gap betw…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…
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.…
We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…
Designs which 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. This mean…
We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models…
Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…
We study the optimal design problems where the goal is to choose a set of linear measurements to obtain the most accurate estimate of an unknown vector in $d$ dimensions. We study the $A$-optimal design variant where the objective is to…
Suppose an $n \times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \ll n$ of the responses, and then produce a…
This paper formulates an input design approach for truncated infinite impulse response identification in the context of implicit model representations recently used as basis for data-driven simulation and control approaches. Precisely, the…
This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of…
e consider the experimental design problem in an online environment, an important practical task for reducing the variance of estimates in randomized experiments which allows for greater precision, and in turn, improved decision making. In…
We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations and, consequently, is computationally expensive to evaluate.…
Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…
We study design-unbiased estimation of the finite-population total $\sum_{i=1}^N y_i$ when each outcome satisfies known bounds $y_i\in[a_i,b_i]$. For any sampling design with inclusion probabilities $\pi_i>0$, we prove a sharp lower bound…
Unbiased and consistent variance estimators generally do not exist for design-based treatment effect estimators because experimenters never observe more than one potential outcome for any unit. The problem is exacerbated by interference and…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
Consider linear regression where the examples are generated by an unknown distribution on $R^d\times R$. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least…