Random Fourier Signature Features
This work addresses a computational problem for researchers and practitioners in machine learning dealing with large-scale time series data, offering a scalable solution with incremental improvements over prior methods.
The paper tackles the computational bottleneck of the signature kernel for sequence similarity, which previously scaled quadratically, by developing a random Fourier feature-based acceleration that achieves linear scaling in sequence length and number while maintaining accuracy on moderate-sized datasets and enabling scaling to up to a million time series.
Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to compute the signature kernel scale quadratically in terms of the length and the number of the sequences. To mitigate this severe computational bottleneck, we develop a random Fourier feature-based acceleration of the signature kernel acting on the inherently non-Euclidean domain of sequences. We show uniform approximation guarantees for the proposed unbiased estimator of the signature kernel, while keeping its computation linear in the sequence length and number. In addition, combined with recent advances on tensor projections, we derive two even more scalable time series features with favourable concentration properties and computational complexity both in time and memory. Our empirical results show that the reduction in computational cost comes at a negligible price in terms of accuracy on moderate-sized datasets, and it enables one to scale to large datasets up to a million time series.