EnhanceD Data stream Analysis: combining the signature method and machine learning algorithms

• Applicant: Professor Dr. Joscha Diehl
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing ; Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 442590525

The analysis of multi-dimensional time series is a fundamental problem in most areas of science and industry. Often, linear models are insufficient to capture the structure present in data. We propose to develop and improve techniques for this problem based on a mathematical object known as the iterated-integrals signature (IIS). Equipped with mathematical guarantees, the IIS is a means to extract (almost all) multilinear features of a time series. It is hence, at least on paper, well-suited to discover non-linear effects indata. Recently, this suspicion has been corroborated by a series of works that successfully apply the IIS in the realm of data science and statistics.Our interdisciplinary team of researchers from machine learning, algebra, stochastic analysis, data assimilation, and oceanography aims to- develop interpretable features of multi-dimensional time-series in a rigorous algebraic framework, based on the IIS, for the analysis of dependence, synchronization, and structure- understand how to extract these features in a robust fashion- develop statistical guaranteesfor these features in the setting of standard time-series modelsand benchmark on synthetic data- use these new - as well as existing - statistical methods to perform original investigation on oceanic and climate data

• DFG Programme: Research Grants
• International Connection: France, Japan
• Partner Organisation: Agence Nationale de la Recherche / The French National Research Agency; Japan Science and Technology Agency; JST
• Cooperation Partners: Professorin Dr. Marianne Clausel; Dr. Nozomi Sugiura