Research school on “Machine Learning and Rough Path Theory for sequential data analysis”

Understanding complex and multi-modal data streams is a key challenge in data science with a broad impact on various real-world applications. Machine learning, in particular deep learning, has achieved considerable progress in analysing streamed data; for example, Recurrent neural networks or the more recent Transformer networks are state-of-the-art sequential models in the fields such as natural language processing and computer vision. Despite their impressive empirical performance, deep learning-based sequential models may face the following difficulties, i.e., (1) lack of interpretability, (2) the need for a large dataset, (3) high computational cost, especially for high-frequency time series data and (4) sensitive to missing data and irregular sampling.

Rough path theory, originating as a branch of stochastic analysis, may offer some insights to address the above challenges as a complementary approach to machine learning. It provides a mathematical approach to summarize complex data streams locally; these principled and parsimonious summaries are robust to irregular time series and may bring massive dimensions to high-frequency data. Incorporating rough path theory into machine learning (e.g., deep learning, kernel methods and neural ODEs) enables the development of a set of novel machine learning tools for sequential data, which often lead to improved accuracy, efficiency and robustness. These emerging techniques have shown superior performance on a number of empirical applications, ranging from online-handwritten character recognition to financial data analysis.
There is an increasing trend of connecting mathematics, not limited to rough path theory, with machine learning methods to develop the theoretical foundations of ML or novel learning algorithms for performance improvement. One can find methods from algebraic topology in topological data analysis, Riemannian geometry in manifold learning, Banach space theory in compressed sensing, tensor algebra in hierarchical decompositions, or graph and hyper-graph theory in network analysis, to name but a few examples.

We want to introduce the participants of this school to those problems and to a wide range of new mathematical techniques, and to prepare them to pursue novel mathematical research.