Inference and Characterization of Causal Structure in Complex Dynamical Systems
| advisor: | Jaroslav Hlinka |
| e-mail: | show e-mail |
| type: | phd thesis |
| branch of study: | MI_MM, MI_AMSM |
| key words: | komplexní systém, kauzalita, stochastické procesy, teorie informace, dynamický systém, teorie grafů |
| link: | http://www.cs.cas.cz/staff/hlinka/ |
| description: | Across many scientific fields—from biology through sociology and economics to communication networks and climatology—researchers face the challenge of effectively characterizing systems that are neither fully regular nor completely random. A particular issue arises in characterizing such complex systems based on time series measurements of key variables reflecting the states of individual subsystems. In practice, numerous methods derived from multivariate statistics, time series analysis, statistical physics, signal processing, information theory, and graph theory are utilized to estimate and further characterize the structure of statistical dependencies (or causal relationships) between individual subsystems. A paradigmatic approach in this domain was proposed by Sir Granger in the 1960s [1], defining one variable as causal towards another if it uniquely contributes to predicting its future state. Initially formulated for two interconnected linear systems in econometrics, the concept has subsequently been generalized to nonlinear systems (using information-theoretic functionals) and more efficient algorithms for estimation from high-dimensional data [2,3]. Several questions remain open for study within this dissertation: What are the advantages of characterizing systems through the structure of causal relationships ("effective connectivity") compared to merely describing dependency structures ("functional connectivity")? How can algorithms for estimating causal relationships in high-dimensional settings be further optimized (e.g., dimension reduction, alternative methods for searching the space of candidate causal ancestors)? How can the theoretical concept of causal relationships be suitably generalized to encompass multifactorial causality (cases where a certain set of variables improves prediction despite each individually providing no predictive benefit) [4]? What is the relationship between methods applied in the measurement space and those in the reconstructed state space? What is the relationship between methods developed for causality detection in deterministic versus stochastic processes? Besides theoretical and computational aspects, the work will include demonstrating developed concepts and methods using real-world complex system such as brain activity data. |
| references: | [1] Granger, C. W. Investigating causal relations by econometric model and cross-spectral methods, Econometrica, Blackwell Publ. Ltd., 1969, 37, 424-438 [2] Sun, J.; Taylor, D. & Bollt, E. M. Causal Network Inference by Optimal Causation Entropy, SIAM Journal on Applied Dynamical Systems, 2015, 14, 73-106 [3] Kořenek, J. and Hlinka, J., 2020. Causal network discovery by iterative conditioning: Comparison of algorithms. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(1). [4] Kořenek, Jakub, Pavel Sanda, and Jaroslav Hlinka. \"Towards Definition of Higher Order Causality in Complex Systems.\" arXiv preprint arXiv:2409.08295 (2024) |
| last update: | 27.04.2025 18:52:11 |
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