RSS Applied Probability Section: Rough path theory in machine learning

RSS Applied Probability Section: Rough path theory in machine learning

Date: Wednesday 26 August 2020, 1.00PM - 4.15PM
Location: Online
Online
Section Group Meeting
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In the era of ‘big data’, numerous data streams are being generated by individual activity, business processes and sensors. Data streams record complex sequences of events and are ubiquitous in everyday life; examples range from electronic financial trading records to human-computer interactions. Statistics and now machine learning have achieved considerable success in working with multimodal data streams. Rough Path Theory (RPT) provide a mathematical approach to the description of complex data streams; an approach that can be efficient, concise, robust to different sampling, assimilate new asynchronous features and is able to accommodate missing data.  There are many contexts where incorporating these tools into the data analysis leads to improved efficiency (sometimes by orders of magnitude), quicker training and reduced power consumption. 
RPT originated as a branch of stochastic analysis. It provides a rigorous framework for the analysis of controlled differential equations (CDEs) driven by highly oscillatory streams. Linear functionals on CDEs are a universally approximating family of functions on streams, that allows simple parameterization and is closed under concatenation. It is well adapted to modern frameworks of data science (optimization, back-propagation) in addition to the intrinsic ability to deal with evolving multi-modal data. 
There are many exciting research questions and applications (e.g. algebraic methods providing a new structure theorem for information contained in streamed data, signature-based deep learning methods providing an efficient methodology for predicting cognitive development from longitudinal brain MRI data).
The RSS is committed to ensuring an inclusive and welcoming environment for all who care about good data and statistics.
 
The aims of the workshop are:
•to present a range of research in RP theory for machine learning.
•to encourage dialogue between researchers from diverse disciplines and backgrounds, focusing on the methodology and applications of analysing complex data streams.
•to explore the potential for future collaboration.

This workshop will showcase mathematical methods and the applications in quantitative finance and human-computer interfaces.

Schedule
13:00 - 13:10     Opening
13:10 - 13:50     Terry Lyons, University of Oxford - Title TBC
13:50 - 14:25     Xin Zhang, South China University of Technology - BrainPSNet: Multi-Stream Neural Network based Infant Cognitive Scores Prediction with Temporal Path Signature Features
14:25 - 15:00    Panel discussion
15:20 - 15:55    Joscha Diehl, University of Greifswald - Tropical quasisymmetric functions in time series analysis
15:55 - 16:30    Josef Teichmann, ETH Zürich - Randomized signature and reservoir computing
16:30 - 16:35    Closing remarks

Abstracts:
Josef Teichmann - Randomized signature and reservoir computing
We connect the paradigm of reservoir computing, i.e. the successful use of certain random dynamical systems for feature extraction, with the theory of signature and randomized signature. We apply our findings to scenario generation in high dimensional markets. (joint work with Christa Cuchiero, Lukas Gonon, Lyudmila Grigoryeva and Juan Pablo Ortega).

Xin Zhang - BrainPSNet: Multi-Stream Neural Network based Infant Cognitive Scores Prediction with Temporal Path Signature Features
There is stunning rapid development of human brains in the first year of life. Some studies have revealed the tight connection between cognition skills and cortical morphology in this period. Nonetheless, it is still a great challenge to predict cognitive scores using brain morphological features, given the overlarge dimensionality of neuroimaging data and issues like small sample size and missing data in longitudinal studies. In this talk, for the first time, we introduce the path signature method to explore the hidden analytical and geometric properties of longitudinal cortical morphology features. A novel BrainPSNet is proposed with stacked differentiable temporal path signature layers to produce informative representations of different time points and various temporal granules for each participant. A multi-stream neural network is then included to combine groups of multi-scales temporal features for predicting the cognitive score. Considering different influences of each brain region on the cognitive function, we design a learning-based attention mask generator to automatically weight corresponding brain regions. Experiments are conducted on a longitudinal dataset within 9 time points. By comparing with several state-of-the-art algorithms, the proposed method achieves the best performance. Furthermore, the relationship between morphological features and cognitive abilities is discussed.

Joscha Diehl - Tropical quasisymmetric functions in time series analysis
Aiming for the systematization of time warping invariant features for sequential data we introduce quasisymmetric functions over any semiring. Over the tropical semiring (or min-plus semiring), this leads to the extraction of certain 'non-smooth' features which might be hard to capture by classical iterated sums/integrals. All objects will be introduced and the talk will be self-contained. I briefly outline how this fits nicely into a deep learning pipeline. This is joint work with Kurusch Ebrahimi-Fard (NTNU Trondheim) and Nikolas Tapia (WIAS Berlin).

 
 
Terry Lyons, University of Oxford - Title TBC
Professor Terry Lyons is the Wallis Professor of Mathematics; he is currently PI of the DATASIG program (primarily funded by EPSRC), he was a founding member (2007) of, and then Director (2011-2015) of, the Oxford Man Institute of Quantitative Finance; he was the Director of the Wales Institute of Mathematical and Computational Sciences (WIMCS; 2008-2011). He came to Oxford in 2000 having previously been Professor of Mathematics at Imperial College London (1993-2000), and before that he held the Colin Maclaurin Chair at Edinburgh (1985-93).
Research interests: Prof Lyons’ long-term research interests are all focused on Rough Paths, Stochastic Analysis, and applications – particularly to Finance and more generally to the summarising of large complex data. More specifically, his interests are in developing mathematical tools that can be used to effectively model and describe high dimensional systems that exhibit randomness as well as the complex multimodal data streams that arise in human activity. Prof Lyons is involved in a wide range of problems from pure mathematical ones to questions of efficient numerical calculation. DATASIG is a project that bridges from the fundamental mathematics to application contexts where novel techniques for analysing streamed data have potential to contribute value; these contexts include mental health, action recognition, astronomy, cyber-security, …
Personal webpage: https://www.maths.ox.ac.uk/people/terry.lyons

 Xin Zhang, South China University of Technology - BrainPSNet: Multi-Stream Neural Network based Infant Cognitive Scores Prediction with Temporal Path Signature Features
Dr. Xin Zhang received her bachelor’s degree from Northwestern Polytechnical University, and Ph.D. degree from Oklahoma State University, U.S. Currently, Dr. Zhang is Associate Professor with School of Electronic and Information Engineering, South China University of Technology. She was the visiting scholar in Bioinformatic Research Imaging Center, University of North Carolina at Chapel Hill from 2018 to 2020. Her research interests include computer vision, pattern recognition, gesture estimation and brain data analysis. She has published more than 30 high-level academic papers, granted for more than ten national patents, won the best paper award in ICCV-HANDS Workshop and the two first prizes in the VIVA international competition. Her research work has been funded by NSFC, Guangdong Province NSF, Guangzhou NSF, MSRA and other organizations. Personal webpage: http://www2.scut.edu.cn/ee_en/2017/0510/c21942a166660/page.htm​

Joscha Diehl, University of Greifswald - Iterated sums and applications
Joscha Diehl finished his Ph.D. on topics in rough path theory at the TU Berlin in 2012 under the supervision of Peter Friz. After several postdoc positions in San Diego, Berlin and Leipzig, he is now Junior professor of Stochastic Analysis at the University of Greifswald. He is mainly interested in applying algebraic methods to topics in stochastic analysis, statistics and data science.
Personal webpage: https://diehlj.github.io/​

Josef Teichmann, ETH Zürich - Randomized signature and reservoir computing
Josef Teichmann is Full Professor in Mathematics at ETH Zurich since 2009. His interests include Machine Learning, especially the mathematical foundation of Machine Learning; Stochastic Analysis; Mathematical Finance; Portfolio Management, as well as Frontier Topics such as Big Data and Fintech.
Personal webpage: https://people.math.ethz.ch/~jteichma/
 
Organised by the RSS Applied Probability Section jointly with the DataSig 

Organisers:
Hao Ni, Department of Mathematics, UCL
Alex Watson, Statistical Science, UCL


 
 
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