Applied Probability section meeting report: Rough path theory in machine learning

On the afternoon of 26 August 2020, the RSS Applied Probability section and DataSig jointly hosted an online meeting on Rough path theory in machine learning. The workshop showcased mathematical methods and their applications in quantitative finance, computer vision and biomedical imaging, and had around 40 participants.

This workshop started with the presentation of Professor Terry Lyons, Wallis Professor of Mathematics at the University of Oxford, who developed the rough path theory since the 1990s. He provided a high-level overview of path signatures and their application in machine learning. The signature emerged as a core concept of rough path theory, as a faithful and concise way to describe complex and unparameterized data streams. Professor Lyons discussed empirical applications such as online Chinese handwriting recognition and landmark-based skeleton video recognition, where the use of signatures as a feature contributes to state-of-the-art results.

The second speaker Dr Xin Zhang from the South China University of Technology gave a talk titled 'BrainPSNet: Multi-Stream Neural Network based Infant Cognitive Scores Prediction with Temporal Path Signature Features'. She introduced the first path signature method to explore the hidden analytical and geometric properties of longitudinal cortical morphology features to predict the infant cognitive scores.

Following this, all speakers took part in a panel discussion, chaired by Dr Thomas Cass (Imperial College) and Dr Hao Ni (University College London). The speakers shared their journeys in rough path theory, discussed big topics in future research and shared thought on how to conduct successful research in the field.

In the second half of the workshop, Dr Joscha Diehl (University of Greifswald) gave a presentation on 'What plays the role of CNN for sequential data'. He introduced quasisymmetric functions over any semiring to derive the systematization of time warping invariant features for sequential data.

The last talk was given by Professor Josef Teichmann of ETH Zürich. He talked about the connection between the paradigm of reservoir computing and the theory of signature and randomized signature, with applications in scenario generation in high dimensional markets.

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