One novel application arises in system identification and statistics. There, the joint problem of identification of both the dynamics and the hidden states given trajectories of measurements of the outputs of a dynamical system is notoriously challenging, because of its inherent non-convexity. Recent work has shown that one can recover these, to guaranteed global optimality, by utilizing a hierarchy of convexifications. (See references below.) This opens entirely new avenues in the system identification and related fields, such as causal learning. In connection with recent work on time-varying convex and non-convex optimization, this also opens new avenues in on-line methods for the problem.

There is a PhD studentship available in related topics, to be supervised by Jakub Marecek and Vyacheslav Kungurtsev (Dept. of Computer Science) and Vladimir Havlena (Dept. of Control Engineering) at the Czech Technical University and is part of a broader collaboration with Imperial College London, Technion – Israel Institute of Technology, National and Kapodistrian University of Athens and others. The position is full time and limited to 4 years. The studentship comes with a monthly salary similar to the average pay in Prague, the Czech Republic (approximately 45000 CZK per month before a notably low tax), and a travel budget. The Czech capital regularly ranks among five European cities within the world's best cities in the world to live in (cf. Time Out Magazine index for 2021) and CTU’s offices are in a centrally-located palace with a view of Prague Castle. For more information, please see https://en.wikipedia.org/wiki/Prague

For the PhD position, we seek candidates with Masters degrees in Statistics, Control Theory, Mathematics, Computer Science, Operations Research, or related disciplines, with excellent mathematical aptitude, as demonstrated by involvement in mathematical olympiads, relevant coursework, or undergraduate research. A preference is given to: – candidates with experience with system identification – candidates with experience in programming in Python We expect to start interviewing candidates as soon as possible, with a view of a start between January and September 2023. Please leave your email address at https://docs.google.com/forms/d/e/1FAIpQLSc7aAmoIuT4J8QZ1kNG6CCFgqRG4oofoLg6hcjaE-EjXRtL_w/viewform?usp=pp_url&entry.2102192120=Ideally+between+January+and+September+2023 contact Jakub via email.

There is also a post-doctoral post available in related topics, with a pay of up to EUR 40000 p.a. Candidates with a PhD system identification or statistics are particularly welcome. To apply for the post-doctoral position, please use the same form.

Czech Technical University (CTU) is the oldest non-military technical university in Europe. In the academic year 2020/21, CTU offered 130 degree programs in Czech and 84 in English. CTU’s Artificial Intelligence Center (AIC) with a staff of 150 is widely recognized as one of the best in the region. CSRankings.org currently ranks it at number 6 in Europe within AI and Computer Vision, after Technion, ETH Zurich, Imperial, Max Planck Society, and EPFL. For more information, please see https://www.aic.fel.cvut.cz/

References: Kozdoba, Marecek, Tchrakian, Mannor: On-Line Learning of Linear Dynamical Systems: Exponential Forgetting in Kalman Filters, AAAI 2020, https://arxiv.org/abs/1809.05870 Zhou, Marecek and Shorten: Fairness in Forecasting and Learning Linear Dynamical Systems, AAAI 2021, https://arxiv.org/abs/2006.07315, and Journal of AI Research 2023, https://arxiv.org/abs/2209.05274 Bellon, Henrion, Kungurtsev, Marecek: Time-Varying Semidefinite Programming: Geometry of the Trajectory of Solutions. https://arxiv.org/abs/2104.05445 Bellon, Dressler, Kungurtsev, Marecek, Uschmajew: Time-Varying Semidefinite Programming: Path Following a Burer--Monteiro Factorization. https://arxiv.org/abs/2210.08387