Deep Signature Transforms
This work addresses the challenge of making signature transforms more flexible and data-adaptive for machine learning practitioners, representing an incremental improvement over existing methods.
The authors tackled the problem of integrating the signature transform, a fixed feature transformation for data streams, with deep learning by proposing a method to learn augmentations before the transform and use it as a neural network layer, achieving empirical results that support theoretical justification.
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a model may be built. We propose a novel approach which combines the advantages of the signature transform with modern deep learning frameworks. By learning an augmentation of the stream prior to the signature transform, the terms of the signature may be selected in a data-dependent way. More generally, we describe how the signature transform may be used as a layer anywhere within a neural network. In this context it may be interpreted as a pooling operation. We present the results of empirical experiments to back up the theoretical justification. Code available at https://github.com/patrick-kidger/Deep-Signature-Transforms.