H2O: Higher-Order pattern-discovery in High-dimensional data

The workshop “H2O: Higher-Order pattern-discovery in High-dimensional data” was highly successful from both the scientific and networking perspectives. The event brought together 35 participants from a broad range of countries, including Germany, Denmark, the United Kingdom, France, the Netherlands, Sweden, and Croatia, and the audience also included an industry representative. Approximately half of the participants were PhD students and postdoctoral researchers. This strong participation by early-career researchers contributed substantially to the lively and constructive atmosphere of the meeting. COST support was essential in enabling us to respond to the high level of interest and to organise the event at a scale that allowed for broad participation and exchange.

The workshop fully achieved its principal objective of bringing together researchers from topological data analysis, time-series analysis, and high-dimensional statistics. These areas often address closely related challenges, but typically from different methodological perspectives. The scientific programme therefore provided an effective framework for knowledge exchange across disciplinary boundaries. The keynote and invited lectures covered a broad spectrum of themes, including persistence-based summaries of complex data, stochastic approximation, random matrix methods, nonparametric inference, jump-process estimation, and change-point detection. Collectively, these contributions highlighted a common interest in identifying meaningful structure in complex, noisy, and high-dimensional observations.

A particularly important outcome of the workshop was the visibility of concrete applications and data-driven challenges. Several contributions demonstrated how advanced mathematical and statistical methods can be brought to bear on relevant real-world problems. These included the analysis of histological breast-cancer tissue images, EEG and intracranial EEG data for the study of brain dynamics, time-varying correlation networks, COVID-19 monitoring, and environmental DNA time series. Other talks addressed topics related to asset pricing, diffusion control, and the statistical analysis of random sets. In this way, the workshop showed clearly that current developments in mathematical statistics are closely connected to applications in health, life sciences, environmental monitoring, and the analysis of complex technological systems.

The poster session played an important role in supporting interaction and capacity building, especially for junior participants. It provided an opportunity for early-career researchers to present their work, receive feedback, and engage directly with senior researchers from neighbouring areas. This contributed to a collegial and open atmosphere throughout the meeting and facilitated a number of promising exchanges concerning future collaborations. The workshop therefore functioned not only as a venue for the presentation of recent results, but also as a platform for community building and knowledge transfer across fields.

More generally, the meeting illustrated how questions related to higher-order structure, dependence, geometry, and dynamics arise naturally across scales and across a broad spectrum of application areas. In this respect, the workshop was well aligned with the wider objectives of mSPACE, in particular the aim of connecting complementary mathematical tools and research communities in order to improve the understanding of complex structured systems. Overall, the event made a meaningful contribution to international networking, interdisciplinary exchange, and the integration of early-career researchers into a broader European research community.