Related papers: Optimal experimental designs for inverse quadratic…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
Mechanistic mathematical models of biological systems usually contain a number of unknown parameters whose values need to be estimated from available experimental data in order for the models to be validated and used to make quantitative…
Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. Here we investigate local optimality. We propose to study for a given design its region of optimality in parameter space.…
Given n experiment subjects with potentially heterogeneous covariates and two possible treatments, namely active treatment and control, this paper addresses the fundamental question of determining the optimal accuracy in estimating the…
Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…
In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear…
In this work the primary objective is to maximize the precision of the maximum likelihood estimate in a linear regression model through the efficient design of the experiment. One common measure of precision is the unconditional mean square…
This paper addresses the inverse optimal control for the linear quadratic tracking problem with a fixed but unknown target state, which aims to estimate the possible triplets comprising the target state, the state weight matrix, and the…
We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural…
The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part…
There have been some major advances in the theory of optimal designs for interference models. However, the majority of them focus on one-dimensional layout of the block and the study for two-dimensional interference model is quite limited…
We consider the problem of efficient statistical inference for comparing two regression curves estimated from two samples of dependent measurements. Based on a representation of the best pair of linear unbiased estimators in continuous time…
Alphabetic optimality criteria, such as the $D$, $A$, and $I$ criteria, require specifying a model to select optimal designs. They are not model free and the optimal designs selected by them are not robust to model uncertainty. Recently,…
We consider optimal experimental design (OED) for Bayesian inverse problems, where the experimental design variables have a certain multiway structure. Given $d$ different experimental variables with $m_i$ choices per design variable $1 \le…
In this paper we extend the results of Radloff and Schwabe (2018), which could be applied for example to Poisson regression, negative binomial regression and proportional hazard models with censoring, to a wider class of non-linear multiple…
We present a unified deterministic approach for experimental design problems using the method of interlacing polynomials. Our framework recovers the best-known approximation guarantees for the well-studied D/A/E-design problems with simple…
In clinical trials, the response of a given subject often depends on the selected treatment as well as on some covariates. We study optimal approximate designs of experiments in the models with treatment and covariate effects. We allow for…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
Fractional polynomial models are potentially useful for response surfaces investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However, as in all…