### Kernels for sequentially ordered data

**2016-01-29**

1601.08169 | stat.ML

We present a novel framework for kernel learning with sequential data of any
kind, such as time series, sequences of graphs, or strings. Our approach is
based on signature features which can be seen as an ordered variant of sample
(cross-)moments; it allows to obtain a "sequentialized" version of any static
kernel. The sequential kernels are efficiently computable for discrete
sequences and are shown to approximate a continuous moment form in a sampling
sense.
A number of known kernels for sequences arise as "sequentializations" of
suitable static kernels: string kernels may be obtained as a special case, and
alignment kernels are closely related up to a modification that resolves their
open non-definiteness issue. Our experiments indicate that our signature-based
sequential kernel framework may be a promising approach to learning with
sequential data, such as time series, that allows to avoid extensive manual
pre-processing.

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