Convolutional Signature for Sequential Data

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.