In this talk, we consider the supervised learning problem 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 characterise 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. We apply it to the example of detecting transient datasets and demonstrate the superior effectiveness of this method benchmarked with supervised learning methods with raw data.
