Project A3: Numerical Methods for Non-Euclidean Minimization Problems Arising in Statistical Feature Reduction
Exponential analysis models have many applications in science and engineering. In recent years there has been a strong interest in Prony-kind methods for parameter estimation and sparse approximation with exponential sums. However, the employed numerical algorithms are usually not consistent. Maximum likelihood modifications of Prony’s method ensure consistency but lead to non-convex minimization problems.
In the first cohort, we derived the operator based Prony method that allows more general sampling schemes for parameter reconstruction. In the second PhD project, we are interested in the statistical behavior of the newly derived exponential analysis tool. In particular, we will consider consistency and asymptotic behavior of the method for different noise distributions. Further, we want to derive more stable numerical algorithms for parameter estimation also for the generalized setting.
Applications: sparse data approximation, shape analysis