Theoretical and Experimental Investigations into Causality, its Measures and Applications

Kathpalia, Aditi (2021) Theoretical and Experimental Investigations into Causality, its Measures and Applications. Doctoral thesis, NIAS.

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Thesis advisorNagaraj,
Abstract: A major part of human scientific endeavour aims at making causal inferences of observed phenomena. While some of the studies conducted are experimental, others are observational, the latter often making use of recorded data. Since temporal data can be easily acquired and stored in today’s world, time-series causality estimation measures have come into wide use across a range of disciplines such as neuroscience, earth science and econometrics. In this context, model-free/data-driven methods for causality estimation are extremely useful, as the underlying model generating the data is often unknown. However, existing data-driven measures such as Granger Causality and Transfer Entropy impose strong statistical assumptions on the data and can only estimate causality by associational means. Associational causality, being the most rudimentary level of causality has several limitations. In this thesis, we propose a novel Interventional Complexity Causality scheme for time-series measurements so as to capture a higher level of causality based on intervention which until now could be inferred only through model-based measures. Based on this interventional scheme, we formulate a Compression-Complexity Causality (CCC) measure that is rigorously tested on simulations of stochastic and deterministic systems and shown to overcome the limitations of existing measures. CCC is then applied to infer causal relations from real data mainly in the domain of neuroscience. These include the study of brain connectivity in human subjects performing a motor task and a study to distinguish between awake and anaesthesia states in monkeys using electrophysiological brain recordings. Through theoretical and empirical advances in causality testing, the thesis also makes contributions to a number of allied disciplines. A causal perspective is given for the ubiquitous phenomenon of chaotic synchronization. One of the major contributions in this regard is the introduction of the notion of Causal Stability and formulation (with proof) of a novel Causal Stability Synchronization Theorem which gives a condition for complete synchronization of coupled chaotic systems. Further, we propose and test for techniques to analyse causality between sparse signals using compressed sensing. A real application is demonstrated for the case of sparse neuronal spike trains recorded from rat prefrontal cortex. The area of temporal-reversibility detection of time-series is also closely linked to the domain of causality testing. We develop and test a new method to check for time-reversibility of processes and explore the behaviour of causality measures on coupled time-reversed processes.
Item Type: Thesis (Doctoral)
Additional Information: Thesis submitted to Manipal Academy of Higher Education, Manipal [Year of Award: 2021] [Thesis No. TH58]
Keywords: Causality, Time Series Analysis, Compression-complexity Causality
Subjects: School of Humanities > Consciousness Studies
Doctoral Programme > Theses
Date Deposited: 30 Jun 2021 18:52
Last Modified: 22 Aug 2023 06:26
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