Tensor Methods for Global Sensitivity Analysis

Abstract

Sobol indices and other, more recent quantities of interest (such as the effective and mean dimensions, the dimension distribution, or the Shapley values) are of great aid in sensitivity analysis, uncertainty quantification, and model interpretation. Unfortunately, computing such indices is still challenging for high-dimensional systems.We propose the tensor train decomposition (TT) as a unified framework for surrogate modeling and sensitivity analysis of independently distributed variables. To this end, we introduce the Sobol tensor train (Sobol TT) data structure, which compactly represents variance components for all possible joint variable interactions of any order. Our formulation allows efficient aggregation and subselection operations, and we are able to obtain related Sobol indices and other related quantities at low computational cost.