Reconstruction of the causal network from time series

PhD study program: Applied Mathematics
Akademic year: 2023-2024
Advisor: RNDr. Anna Krakovská, CSc. (krakovska@savba.sk)
External educational institution: Institute of Measurement Science SAS
Accepting university: Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Department of Applied Mathematics and Statistics

Annotation:

Detecting causal relationships from time series is an emerging topic in many scientific disciplines. The topic brings theoretical challenges, as well as an opportunity to design new methods and test them on real measurements. Emphasis will be placed on the development of a methodology for causal detection, taking into account the nature of the investigated processes (stochastic, fractal, deterministic, or combined). Research problems to be explored include distinguishing direct and indirect effects, revealing the presence of unobserved confounders, assessing the differences in complexity between driving and driven systems, etc. From the application point of view, multichannel electroencephalographic recordings from the human brain, multi-lead ECG measurements, extensive sets of climate measurements, time evolution of a set of economic indicators and other real problems of finding causal relationships from measured time series are of particular interest. The topic is suitable for graduates interested in creative application and development of relevant mathematical approaches. The successful candidate must also have good English skills, as well as experience in creating and testing software in MATLAB. As part of the doctoral studies, the student will expand his/her knowledge in the field of bio-measurements and become familiar with some methods from the theory of dynamical systems, including chaos and fractal theory, and partially also from statistics, information theory, and mathematical optimization. The dissertation will be completed at the Institute of Measurement Science of the Slovak Academy of Sciences in Bratislava.

The aim of the dissertation is to develop a methodology of causal detection in order to reconstruct the causal network, if the nodes of the network are characterized by time series.