Identifying causal dependencies in multivariate functional data with applications in socioeconomics
File(s)
Author(s)
Laumann, Felix
Type
Thesis
Abstract
The presented doctoral research aims to develop novel statistical methods to learn causal graphs from observational data of function-valued random variables, and apply them to socioeconomic data sets.
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to engineering and socioeconomics.
Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum.
Traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension.
We first extend the applicability of kernel-based two-sample and bivariate independence tests to nonstationary random processes, a special class of functional data, by assuming access to independent realisations of the underlying smooth process. Kernel-based independence tests, which form the cornerstone of regression- and constraint-based causal structure learning methods, are then extended to be applicable to any functional data.
By applying specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence on function-valued random variables. When these independence tests are then used in causal structure learning algorithms, empirical results on synthetic data demonstrate higher accuracies when compared to established methods like Granger-causality, convergent cross mappings or the PC algorithm with momentary conditional independence. Socioeconomic systems are generally assumed to entail complex interactions. Using the aforementioned independence tests, we investigate undirected interactions amongst the Sustainable Development Goals and climate change, measured by 400 variables in 181 countries over 20 years.
We then utilise a network representation to identify the most important objectives (using network centrality) and to obtain nexuses of objectives (defined as highly interconnected clusters). Moreover, we evaluate the World Governance Indicators for directed interactions amongst its six variables using data from 182 countries over 25 years.
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to engineering and socioeconomics.
Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum.
Traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension.
We first extend the applicability of kernel-based two-sample and bivariate independence tests to nonstationary random processes, a special class of functional data, by assuming access to independent realisations of the underlying smooth process. Kernel-based independence tests, which form the cornerstone of regression- and constraint-based causal structure learning methods, are then extended to be applicable to any functional data.
By applying specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence on function-valued random variables. When these independence tests are then used in causal structure learning algorithms, empirical results on synthetic data demonstrate higher accuracies when compared to established methods like Granger-causality, convergent cross mappings or the PC algorithm with momentary conditional independence. Socioeconomic systems are generally assumed to entail complex interactions. Using the aforementioned independence tests, we investigate undirected interactions amongst the Sustainable Development Goals and climate change, measured by 400 variables in 181 countries over 20 years.
We then utilise a network representation to identify the most important objectives (using network centrality) and to obtain nexuses of objectives (defined as highly interconnected clusters). Moreover, we evaluate the World Governance Indicators for directed interactions amongst its six variables using data from 182 countries over 25 years.
Version
Open Access
Date Issued
2023-11
Date Awarded
2024-05
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Barahona, Mauricio
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)