Jiaqi Wang The minimum covariance determinant (MCD) problem selects a fixed-cardinality subset of data points to minimize its sample covariance determinant. We develop approximation and exact algorithms and apply them to prediction residuals, using the mean and covariance of the selected subset to define ellipsoidal conformal regions. For rational data, quadratic-form selection yields a deterministic approximation scheme … Read more
Modern experimentation in business and public policy often studies targeted interventions whose effects depend on the heterogeneous attributes of individuals. We examine heterogeneous treatment effects through the lens of optimal design of experiments, which allocates treatment decisions to maximize the precision of estimated treatment-covariate interactions. We introduce the D-optimal partitioning problem for balancing the information … Read more
The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite support — a regime that frequently arises in machine learning and operations research. The discrete Wasserstein barycenter problem is known to … Read more