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Cumulative link models have been widely used for ordered categorical responses. Uniform allocation of experimental units is commonly used in practice, but often suffers from a lack of efficiency. We consider D-optimal designs with ordered…
Design of experiments is a fundamental topic in applied statistics with a long history. Yet its application is often limited by the complexity and costliness of constructing experimental designs, which involve searching a high-dimensional…
We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the…
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…
Traditional model-free feature selection methods treat each feature independently while disregarding the interrelationships among features, which leads to relatively poor performance compared with the model-aware methods. To address this…
In confirmatory clinical trials with small sample sizes, hypothesis tests based on asymptotic distributions are often not valid and exact non-parametric procedures are applied instead. However, the latter are based on discrete test…
A high-ranking goal of interdisciplinary modeling approaches in the natural sciences are quantitative prediction of system dynamics and model based optimization. For this purpose, mathematical modeling, numerical simulation and scientific…
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the…
We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: To each point of a design is attached a binary label that…
We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements…
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…
We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $L^2$ norm and $H^1$ weighted…
We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
We study the problem of deleting user data from machine learning models trained using empirical risk minimization. Our focus is on learning algorithms which return the empirical risk minimizer and approximate unlearning algorithms that…
Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is \emph{a priori} known or suspected that a subset of the covariates do not significantly contribute to the overall fit of…
We consider a class of misspecified dynamical models where the governing term is only approximately known. Under the assumption that observations of the system's evolution are accessible for various initial conditions, our goal is to infer…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…