Convolutional Signature for Sequential Data

Signature is an infinite graded sequence of statistics known to characterize geometric rough paths. While the use of the signature in machine learning is successful in low-dimensional cases, it suffers from the curse of dimensionality in high-dimensional cases, as the number of features in the truncated signature transform grows exponentially fast. With the idea of Convolutional Neural Network, we propose a novel neural network to address this problem. Our model reduces the number of features efficiently in a data-dependent way. Some empirical experiments including high-dimensional financial time series classification and natural language processing are provided to support our convolutional signature model.