2024/01/05 by Khadija Musayeva, Musayeva, Khadija, Mickaël Binois +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Control Systems and Identification #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.2401.02735
openalex publication_date 2024/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper proposes several approaches as baselines to compute a shared active subspace for multivariate vector-valued functions. The goal is to minimize the deviation between the function evaluations on the original space and those on the reconstructed one. This is done either by manipulating the gradients or the symmetric positive (semi-)definite (SPD) matrices computed from the gradients of each component function so as to get a single structure common to all component functions. These approaches can be applied to any data irrespective of the underlying distribution unlike the existing vector-valued approach that is constrained to a normal distribution. We test the effectiveness of these methods on five optimization problems. The experiments show that, in general, the SPD-level methods are superior to the gradient-level ones, and are close to the vector-valued approach in the case of a normal distribution. Interestingly, in most cases it suffices to take the sum of the SPD matrices to identify the best shared active subspace.