Computing Active Subspaces Efficiently with Gradient Sketching by Paul G. Constantine, Armin Eftekhari, Michael B. Wakin
Active subspaces are an emerging set of tools for identifying and exploiting the most important directions in the space of a computer simulation's input parameters; these directions depend on the simulation's quantity of interest, which we treat as a function from inputs to outputs. To identify a function's active subspace, one must compute the eigenpairs of a matrix derived from the function's gradient, which presents challenges when the gradient is not available as a subroutine. We numerically study two methods for estimating the necessary eigenpairs using only linear measurements of the function's gradient. In practice, these measurements can be estimated by finite differences using only two function evaluations, regardless of the dimension of the function's input space.
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.