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Deep Signature Transforms
Patrick Kidger · Patric Bonnier · Imanol Perez Arribas · Cristopher Salvi · Terry Lyons

Wed Dec 11 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #126

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 \texttt{github.com/patrick-kidger/Deep-Signature-Transforms}.

Author Information

Patrick Kidger (University of Oxford)
Patric Bonnier (University of Oxford)
Imanol Perez Arribas (University of Oxford)
Cristopher Salvi (University of Oxford)
Terry Lyons (University of Oxford)

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