In the fight against money laundering, demand for data-driven Anti-Money Laundering (AML) solutions is growing. Particularly anomaly detection algorithms have proven effective in the detection of suspicious customer behaviour, as well as observing patterns otherwise hidden in customer transaction data. In this thesis, the Isolation Forest anomaly detection algorithm is studied in combination with the model-specific local explanation method, Multiple Indicator Local Depth-based Isolation Forest Feature Importance (MI-Local-DIFFI). To expand Isolation Forest to mixed-attribute data sets, the incorporation of nominal features is explored in more detail. This analysis resulted in the introduction of Isolation Forest with Categorical Sampling (iForestCS ), a methodology that directly incorporates nominal attributes into an isolation tree without the need of encoding it onto a numerical scale. This method is tested against different encoding strategies and Isolation Forest Conditional Anomaly Detection (iForestCAD) using different synthetic data sets. The method shows improved performance to the utilization of encoding strategies for different parameters of the underlying synthetic data. Furthermore, this thesis explores the potential of ternary Isolation Forest, in which the branching strategy of an isolation tree is expanded to produce three child nodes. It is demonstrated using synthetic data, that particularly the performance of MI-Local-DIFFI reduces when applied to a ternary Isolation Forest. Finally, the research considers a practical use-case. Using customer transaction data from Triodos Bank, the locally explainable Isolation Forest is applied to mixed-attribute customer transaction data. This has provided useful insight and resulted in the detection of suspicious customer behaviour and the introduction of new rules into business practices. Although the most interesting customer behaviour did not directly emanate from the nominal attributes, the method of incorporating nominal features resulted in differences when considering the anomalies with the highest anomaly scores.

By sampling financial correlation matrices over sliding windows, it has been shown in recent work that the quantum majorization induced partial ordering on this space of correlation matrices known as the "quantum Lorenz ordering" (QLO) can be used to characterize systemic risk by clustering correlation matrices according to their degree centrality on the associated directed graph called the "quantum majorization graph" (QMG). In this work, clusterings of the QMG are used to construct an online Bayesian nonparametric alarm system for the prediction of stock market crashes via the so-called "reinforced urn process" (RUP). To test the efficacy of this modelling methodology we exploit extreme value theory to systematically define stock market crashes by studying the tail of an appropriately fitted generalized pareto distribution (GPD) for stock market drawdowns. This approach identified 13 extreme drawdowns between 1985-2020, for which the RUP was trained from 1986-2005 to predict the 8 extreme drawdowns from 2005-2020. Of the three correlation metrics used to test this approach, the QLO corresponding to the set of upper Tail-Dependence matrices was shown to outperform the others: Pearson's and the Gini correlation. Tail-Dependence was able to predict all 8 crashes with just 5 false alarms over a 12 month time horizon, all 8 with 7 false alarms over an 8 month time horizon, 7 out of 8 with 9 false alarms over a 4 time horizon, and 7 out of 8 with 17 false alarms over a 2 month time horizon. This approach was then tested against the usage of the Log-Periodic Power Law Singularity (LPPLS) model's confidence indicators with promising results. The quantum Lorenz ordering is meant to rank a set of correlation matrices by the amount of dispersion reflected in their spectra: a true heterogeneity. We consider this dispersion from the standpoint of measurement error as has been in the application of random matrix theory (RMT) to correlation matrices in portfolio risk theory. We provide analytical relations between quantum majorization and random matrix cleaning for a few RMT filtering schemes posing quantum majorization as a desirable condition for RMT filtering. The RUP is tested using these RMT cleaned correlation matrices as well.