Deep signature transforms
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 combi...
| Main Authors: | , , , , |
|---|---|
| Format: | Conference item |
| Language: | English |
| Published: |
Curran Associates
2019
|
| _version_ | 1826294587471167488 |
|---|---|
| author | Bonnier, P Kidger, P Perez Arribas, I Salvi, C Lyons, T |
| author_facet | Bonnier, P Kidger, P Perez Arribas, I Salvi, C Lyons, T |
| author_sort | Bonnier, P |
| collection | OXFORD |
| description | 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 github.com/patrick-kidger/Deep-Signature-Transforms. |
| first_indexed | 2024-03-07T03:47:58Z |
| format | Conference item |
| id | oxford-uuid:c02d4f18-30e6-4c89-9c65-ecc56978c6d8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:47:58Z |
| publishDate | 2019 |
| publisher | Curran Associates |
| record_format | dspace |
| spelling | oxford-uuid:c02d4f18-30e6-4c89-9c65-ecc56978c6d82022-03-27T05:52:49ZDeep signature transformsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:c02d4f18-30e6-4c89-9c65-ecc56978c6d8EnglishSymplectic Elements at OxfordCurran Associates2019Bonnier, PKidger, PPerez Arribas, ISalvi, CLyons, TThe 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 github.com/patrick-kidger/Deep-Signature-Transforms. |
| spellingShingle | Bonnier, P Kidger, P Perez Arribas, I Salvi, C Lyons, T Deep signature transforms |
| title | Deep signature transforms |
| title_full | Deep signature transforms |
| title_fullStr | Deep signature transforms |
| title_full_unstemmed | Deep signature transforms |
| title_short | Deep signature transforms |
| title_sort | deep signature transforms |
| work_keys_str_mv | AT bonnierp deepsignaturetransforms AT kidgerp deepsignaturetransforms AT perezarribasi deepsignaturetransforms AT salvic deepsignaturetransforms AT lyonst deepsignaturetransforms |