Kernels for Sequentially Ordered Data
Franz J. Kiraly, Harald Oberhauser; 20(31):1−45, 2019.
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.
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