Convolutional Signature for Sequential Data
This addresses a computational bottleneck for researchers and practitioners using signature methods in machine learning, though it appears incremental as it builds on existing signature and CNN concepts.
The paper tackles the exponential feature growth in truncated signature transforms for high-dimensional sequential data by proposing a novel neural network model inspired by Convolutional Neural Networks, which reduces features efficiently in a data-dependent way, with empirical experiments supporting the model.
Signature is an infinite graded sequence of statistics known to characterize geometric rough paths, which includes the paths with bounded variation. This object has been studied successfully for machine learning with mostly applications in low dimensional cases. In the high dimensional case, it suffers from exponential growth in the number of features in truncated signature transform. We propose a novel neural network based model which borrows the idea from Convolutional Neural Network to address this problem. Our model reduces the number of features efficiently in a data dependent way. Some empirical experiments are provided to support our model.