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Kernels for sequentially ordered data

Király, FJ; Oberhauser, H; (2019) Kernels for sequentially ordered data. Journal of Machine Learning Research , 20 (31) pp. 1-45. Green open access

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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 > 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.ucl.ac.uk/id/eprint/1517407
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