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School of Mathematical Sciences

Novel causal models for multivariate functional data

Supervisor: Dr Eftychia Solea

Project description:
Multivariate functional data, where continuous observations are sampled from a vector of stochastic processes, have become increasingly common with the rise of Big Data.  For example, functional magnetic resonance imaging (fMRI) provides brain signals measured over a time domain for thousands of voxels in the brain. Causal reasoning is fundamental in scientific research and engineering, but existing causal learning techniques focus on rectors and are not applicable to functional data, which could mean missed opportunities for insights.  The project addresses this challenge by developing a class of novel causal statistical models and associated theory for discovering causality from multivariate functional data. It will address the limitations of today’s analyses in causality that focus on random vectors. This research is timely as it responds to the growing demands and needs for adequate statistical analysis of samples of complex data and aligns with the themes of Al & Data Modelling.  The work is expected to benefit a wide range of applications including, neuroimaging, bioinformatics, social and behavioural sciences, econometrics, and energy industry.

This multidisciplinary project proposes a class of novel statistical methods for learning causality from large, complex, and highly structured data in the form of functions. These tools are essential in the era of big data. The project will study two set of problems: (1) functional causal inference and functional causal mediation analysis for estimating and inferring the direct and indirect causal effects among functions; and (2) functional directed acyclic graphical modelling for estimating directional associations among functions.  To this end, the project will combine recent developments in functional data analysis with causal learning techniques.  This area is essentially unexplored, yet it opens new perspectives for causal inference and causal graphical modelling based on large-scale and complex multivariate functional data. The work will study asymptotic properties of these new estimators, statistical inference procedures, and efficient algorithms to implement these methods. The algorithms to be developed will be made publicly available for reproducibility and further research.  The asymptotic theory and the computational algorithms will lead to the creation of a toolbox useful for multiple fields, including functional data analysis, causality, statistics, graphical modelling, and machine learning.

Further information: 
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