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| Title | The signature based approach to the supervised learning problems on the paths space |
| Time | 14:00 - 15:00, 21 Nov 2018 |
| Venue | DSI Boardroom, DSI, William Penney Lab, South Kensington Campus, Imperial College. |
| Content | Regression analysis aims to use observational data from multiple observations to develop a functional relationship relating explanatory variables to response variables, which is important for much of modern statistics, and econometrics, and also the field of machine learning. In this talk, we consider the special case where the explanatory variable is a data stream. We provide an approach based on identifying carefully chosen features of the stream which allows linear regression to be used to characterize the functional relationship between explanatory variables and the conditional distribution of the response; the methods used to develop and justify this approach, such as the signature of a stream and the shuffle product of tensors, are standard tools in the theory of rough paths and provide a unified and non-parametric approach with potential significant dimension reduction.To further improve the efficiency of the signature method, we can combine the non-linear regression method (e.g. recurrent neural network) with the signature feature set. It has the theoretical justification based on numerical approximation theory. Numerical examples are provided to show the superior performance of the proposed method. Lastly I will show that the signature based method have achieved the state-of-the-art results in online handwritten text recognition and action recognition. |
| URL | Page Link |