  The development of machine learning algorithms in the cyber security domain
has been impeded by the complex, hierarchical, sequential and multimodal nature
of the data involved. In this paper we introduce the notion of a streaming tree
as a generic data structure encompassing a large portion of real-world cyber
security data. Starting from host-based event logs we represent computer
processes as streaming trees that evolve in continuous time. Leveraging the
properties of the signature kernel, a machine learning tool that recently
emerged as a leading technology for learning with complex sequences of data, we
develop the SK-Tree algorithm. SK-Tree is a supervised learning method for
systematic malware detection on streaming trees that is robust to irregular
sampling and high dimensionality of the underlying streams. We demonstrate the
effectiveness of SK-Tree to detect malicious events on a portion of the
publicly available DARPA OpTC dataset, achieving an AUROC score of 98%.
