Ryan Cory-Wright We revisit the problem of ensuring strong test-set performance via cross-validation. Motivated by the generalization theory literature, we propose a nested k-fold cross- validation scheme that selects hyperparameters by minimizing a weighted sum of the usual cross-validation metric and an empirical model-stability measure. The weight on the stability term is itself chosen via a nested … Read more
Inspired by the impact of the Goemans-Williamson algorithm on combinatorial optimization, we construct an analogous relax-then-round strategy for low-rank optimization problems. First, for orthogonally constrained quadratic optimization problems, we derive a semidefinite relaxation and a randomized rounding scheme that obtains provably near-optimal solutions, building on the blueprint from Goemans and Williamson for the Max-Cut problem. … Read more
The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. In recent years, data-driven scientific discovery has emerged as a viable competitor in … Read more
Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To select the sparsity and robustness of linear regressors, techniques like k-fold cross-validation are commonly used for hyperparameter tuning. However, cross-validation substantially increases the … Read more
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly scalable and often identifying high-quality solutions, do not possess any optimality guarantees. We reexamine matrix completion with an optimality-oriented eye. We reformulate … Read more
Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain due to fluctuating demand and estimated as a sample average from historical data. This problem is computationally challenging, and instances with as few as 100 … Read more
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves solving a sparsity and orthogonality-constrained convex maximization problem, which is extremely computationally challenging. Most existing works address sparse PCA via methods—such as iteratively computing … Read more
Problem definition: We present our collaboration with the OCP Group, one of the world’s largest producers of phosphate and phosphate-based products, in support of a green initiative designed to reduce OCP’s carbon emissions significantly. We study the problem of decarbonizing OCP’s electricity supply by installing a mixture of solar panels and batteries to minimize its … Read more