Motifs and Manifolds Statistical and Topological Machine Learning for Characterising and Classifying Biomedical Time Series

The increased focus on evidence-based practice in the health sciences led to a plethora of (un)organised and digitised data. In conjunction with the availability of technological advances in the life sciences, this resulted in extraordinary access to biomedical data. Due to efficient measurement devices, the frequency at which data can be obtained is at an unprecedented high, leading to the adage that data, indeed, could be the new gold. Examples of such high-resolution time series data are the continuous monitoring of patient vital parameters or a single electrocardiogram (ECG) itself. The temporal component introduced by time series data is both a chance and a challenge, necessitating the development of appropriate data analysis techniques. A chance, as it allows us to utilise a measurement’s temporal evolution to characterise or classify the object of interest (e.g. patients, cells, or other organisms). A challenge because local and global correlation structures exacerbate obtaining a complete picture of a time-evolving phenomenon. Moreover, many dynamically changing systems exhibit alterations that occur at multiple scales and in multiple channels. This thesis presents a set of novel methods to help characterise and classify time-varying data with the express purpose of answering questions at the intersection of machine learning and healthcare. Recognising that time series arise from different categories, we first separate them into real-valued and object-valued time series and investigate both types separately. For the analysis of the first type, we propose a novel method to mine time series patterns efficiently. Driven by a statistical approach, we will introduce a way to identify temporal biomarkers and illustrate their utility in a data set of intensive care unit patients. For this, we leverage the expressive power of subsequences to obtain a high-dimensional time series representation. This feature representation is subsequently used to develop a kernel method based on optimal transport theory. The developed algorithm is of general applicability for medium-sized data sets and has proven particularly effective in the classification setting. The first part of this thesis ends with the presentation of a collaborative machine learning system to predict myocardial ischaemia from stress test ECGs. We develop a deep learning-based approach to significantly reduce the number of patients that unnecessarily undergo myocardial perfusion imaging. A subsequent interpretability analysis presents a potential path towards explainable and trustworthy artificial intelligence in cardiology. The second part of this thesis describes an effort to improve our understanding of artificial neural networks. By treating the network as a composition of time-varying graphs, we develop a method that characterises the change of its structural complexity over time. Our method captures the benefit of deep-learning best practices and can be used as an earlystopping criterion without the need for a validation data set. We thus manage to improve our understanding of artificial neural networks and shed light on the properties linked to their generalisation capabilities. Throughout this thesis, we demonstrate and highlight that in the analysis of (biomedical) time series, it is crucial to take the end-user into account. Interpretability and statistical analyses are of utter importance to make the otherwise opaque field of machine learning transparent to clinicians, physicians, and biologists. Moreover, we also hold up the mirror to ourselves as machine learning researchers: Comprehending the underlying mechanisms of our algorithms is at least as important as their empirical successes. The present thesis paves the path towards a better understanding of artificial neural networks and sheds light on complex phenotypes such as sepsis and myocardial ischaemia in clinically relevant ways