June 29th, 2022
Prof. Giovanni Motta,, opens an external URL in a new window Texas A&M University
√2-Estimation for Smooth Eigenvectors of Matrix-Valued Functions

Abstract: Modern statistical methods for multivariate time series rely on the eigendecomposition of time-varying covariance as well as the spectral density matrices. The curse of indeterminacy or miss-identification of smooth eigenvector functions has not received much attention. We resolve this important problem and recover smooth trajectories by examining the distance between successive eigenvectors. We change the sign of the next eigenvector if its distance with the current one is larger than the square root of 2. In the case of distinct eigenvalues, this simple method delivers smooth eigenvectors. In the case of coalescing eigenvalues, additional swapping and bridging around the coalescing points are needed. We establish consistency and rates of convergence for the proposed smooth eigenvector estimators. We provide simulation results and applications to real data, where we show that our approach is needed to obtain smooth eigenvectors.

March 16th, 2022
Prof. Alois Steindl,, opens an external URL in a new window TU Wien.
Optimal control of a space rendezvous

Abstact: We consider the transfer of a chaser vehicle to a space station using impulsive control with minimal fuel consumption. It is assumed that the space station moves on a circular Keplerian orbit in a rotational symmetric gravitational field and that the chaser vehicle has already reached the station's orbital plane. The vehicle is steered by impulsive burns of the rockets. The problem is solved numerically using Pontryagin's maximum principle for impulsive controls by a multiple shooting method and a continuation procedure to study the variation of the optimal control strategy for varying time constraints. The problem is studied using a local linearized system and the fully nonlinear system using local Cartesian and polar coordinates.

January 19th, 2022
Prof. Thomas Gärtner, TU Wien.
Effective Machine Learning with Structured Data

Abstract: In this talk I will give an overview of our contributions to effective machine learning with structured data. By structured data we mean data that has no canonical representation in a Euclidean space in which the distance satisfies our intuitive requirements. Such data includes social networks, molecules, resonance spectra, and gene sequences. Regarding effectiveness of machine learning we consider the computational, query, and sample complexity of the machine learning algorithm as well as regret bounds and response time.