🤖 AI Summary
Financial regulation faces challenges in modeling high-dimensional, heterogeneous institutional data with missing values, where conventional methods fail to achieve robust and interpretable structured compression. This paper proposes the first Lloyd-type clustering framework tailored for probability distributions, introducing a novel generalized Wasserstein centroid and establishing a metric system in distribution space based on the generalized Wasserstein distance. This approach effectively addresses data incompleteness and distributional heterogeneity. By mapping financial institutions onto geometrically interpretable risk clusters, the method significantly enhances clustering robustness and interpretability on real-world regulatory datasets. It enables more precise and efficient risk identification and regulatory response, thereby supporting actionable supervision.
📝 Abstract
The increasing availability of granular and big data on various objects of interest has made it necessary to develop methods for condensing this information into a representative and intelligible map. Financial regulation is a field that exemplifies this need, as regulators require diverse and often highly granular data from financial institutions to monitor and assess their activities. However, processing and analyzing such data can be a daunting task, especially given the challenges of dealing with missing values and identifying clusters based on specific features. To address these challenges, we propose a variant of Lloyd's algorithm that applies to probability distributions and uses generalized Wasserstein barycenters to construct a metric space which represents given data on various objects in condensed form. By applying our method to the financial regulation context, we demonstrate its usefulness in dealing with the specific challenges faced by regulators in this domain. We believe that our approach can also be applied more generally to other fields where large and complex data sets need to be represented in concise form.
