Deep Signature Transforms

Abstract

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.

Published at NeurIPS 2019

References in corpus (8)

• Generative Moment Matching Networks
• Training generative neural networks via Maximum Mean Discrepancy optimization
• Rough paths, Signatures and the modelling of functions on streams
• Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU
• Extracting information from the signature of a financial data stream
• Signature moments to characterize laws of stochastic processes
• The iisignature library: efficient calculation of iterated-integral signatures and log signatures
• Derivatives pricing using signature payoffs

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