Hanoi, 2024 February, 2023
Website: http://math.ac.vn/conference/MLRPT2023
1. Aim and objective
The purpose of the research school entitled “Machine Learning and Rough Path Theory for sequential data analysis” (MLxRPT for abbreviation) is to showcase the recent development of Rough path theory (RPT) in machine learning (ML) for understanding complex multimodal data streams. This 5day spring school is composed of 8 minicourses delivered by leading experts in this field, to cover topics from methodological innovation to realworld applications. Two invited keynote talks, along with a panel discussion, will further broaden the scope of the minicourses and stimulate the discussion on general mathematical approaches (e.g., geometry) in ML and data science. The target participants are PhD students and earlycareer researchers with interests in mathematics and data science (especially rough path theory and machine learning for sequential data). This spring school will provide an intellectually stimulating environment for the participants, in particular those from Viet Nam and neighbouring countries in Asia. The participants will benefit from the exposure to the latest research in this field and enjoy the excellent network opportunity. We encourage women and nonbinary people to join our spring school to promote gender balance in mathematics.
2. Description of the scientific content
Understanding complex and multimodal data streams is a key challenge in data science with a broad impact on various realworld 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 stateoftheart sequential models in the fields such as natural language processing and computer vision. Despite their impressive empirical performance, deep learningbased 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 highfrequency 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 highfrequency 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 onlinehandwritten 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 hypergraph 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.
3. School location
Institute of Mathematics, Hanoi (IMH), Vietnam Academy of Science and Technology (VAST). Address: 18 Hoang Quoc Viet Road, Cau Giay disctrict, 10307 Ha Noi, Vietnam. Website: www.math.ac.vn
The conference will be organised in the hybrid form (both online and offline meeting).
4. Sponsors:
We are greatful to receive financial support from the following institutions:
 Institute of Mathematics, VAST.
 International Center for Research and Postgraduate Training in Mathematics under the auspices of UNESCO, Institute of Mathematics, VAST
 MaxPlanckInstitute for Mathematics in the Sciences.
 DataSig group
5. Organisers
Scientific Committee
 Juergen Jost, Max Planck Institute for Mathematics in the Sciences, Germany
 Terry Lyons, University of Oxford, UK.
Organising comittee
 Duc Luu, MPI MIS  Germany & Institute of Mathematics, VAST, Vietnam
 Hao Ni, University College London, UK
 Viet Hung Pham, Institute of Mathematics, VAST, Vietnam
6. Lecturers
Key note talks
 Terry Lyons – University of Oxford: “The connection between rough paths and data science”.
 Juergen Jost – MIS: “Mathematical approaches for the analysis of data”.
Minicourses
 Harald Oberhauser – University of Oxford: “Describing laws of stochastic processes with expected signature moments and cumulants”.
 Thomas Cass, Imperial College London, UK: "Topologies and functions on unparameterised path space"
 Maud Lemercier – University of Oxford: "Signature Kernel Methods".
 Cristopher Salvi  Imperial College: "Infinite widthdepth regimes of Recurrent ResNets."
 Emilio Rossi Ferrucci – University of Oxford: Foundation of rough path theory.
 Yue Wu  University of Strathclyde: “An introduction to the logODE method”.
 Hao Ni  University College London: “Generative models for time series generation: a rough path approach”.
 Weixin Yang (University of Oxford): "Developing the path signature methodology and its applications to some realworld machine learning challenges"
 Duc Luu MPIMIS & IMHVAST: Tracking attractors via discrete rough paths
 Nam Vo  Vin BigData: Machine Learning Methods for the Understanding of the Human Genome
Panel session
 Panel session (Friday afternoon 24/2/2023): Potential mathematical research directions in data analysis.
Programme (to be updated)
7. Registration
