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Title: Partially-observed networks : inference and dynamics
Author: Hoffmann, Till
ISNI:       0000 0004 7963 7302
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2018
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Observing networks completely is not always possible or practical. However, attributes of nodes can help us predict how they interact with one another---even when only partial observations are available. Based on this premise, we discuss four core concepts in this thesis. First, we model individuals as inhabitants of a social space spanned by their demographic attributes who connect with one another based on an unknown connectivity kernel. We develop the statistical techniques to learn the kernel from ego networks and infer friendship preferences from eleven survey datasets from the United Kingdom and the United States, as well as data we collected in three online surveys. Second, we use the kernel to develop an intuitive segregation measure applicable to discrete attributes, such as gender or ethnicity, and continuous attributes, such as age or income. For certain kernels, the measure reduces to a metric that allows us to quantify distance in a multidimensional social space. Third, we show that linear dynamics on large, spatially-embedded networks with a known connectivity kernel can be approximated by convolutional partial differential equations. We illustrate the spatial mean-field theory with two synthetic examples, demonstrate that coupled oscillators on networks behave wave-like at large scales, and test the approximation on a location-based social network. Finally, we develop a model-based community detection algorithm for time series. The hierarchical model allows us to propagate uncertainties from the raw data to community labels. We use the model evidence to automatically determine the number of communities and show that we can recover communities from simulated data even when the number of observations is small. We apply our approach to daily returns of the constituents of the S\&P 100 index to identify communities of stocks with similar behaviour.
Supervisor: Jones, Nick Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral