Király, FJ;
Oberhauser, H;
(2019)
Kernels for sequentially ordered data.
Journal of Machine Learning Research
, 20
(31)
pp. 1-45.
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Abstract
We present a novel framework for learning with sequential data of any kind, such as multivariate time series, strings, or sequences of graphs. The main result is a ”sequentialization” that transforms any kernel on a given domain into a kernel for sequences in that domain. This procedure preserves properties such as positive definiteness, the associated kernel feature map is an ordered variant of sample (cross-)moments, and this sequentialized kernel is consistent in the sense that it converges to a kernel for paths if sequences converge to paths (by discretization). Further, classical kernels for sequences arise as special cases of this method. We use dynamic programming and low-rank techniques for tensors to provide efficient algorithms to compute this sequentialized kernel.
| Type: | Article |
|---|---|
| Title: | Kernels for sequentially ordered data |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://jmlr.org/papers/v20/16-314.html |
| Language: | English |
| Additional information: | License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v20/16-314.html. |
| Keywords: | Sequential data, kernels, signature, ordered moments, signature kernels |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1517407 |
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