A sensitivity matrix based methodology for inverse problem formulation

By A. Cintrón-Arias, H. Banks, A. Capaldi, Alun L. Lloyd. 2020

122 citations recorded by the source corpus.

Abstract We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1% of the estimate.

Subfields: Applied Mathematics, Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/86f83c08cfe35abdc8f7dc402fa3e7d8b570fb82

Citations in the corpus

• CLeaR: A Unified Framework for Resolving the Leakage-Degradation Dilemma in Style Transfer (2026, unknown): “These perspectives are consistent with recent evidence on complementary encoder biases and ensemble diversity, as well as standard identifiability analyses in inverse problems [14, 44, 25, 5].”