We investigate the detection of botnet command and control (C2) hosts in massive IP traffic using machine learning methods. To this end, we use NetFlow data -- the industry standard for monitoring of IP traffic -- and ML models using two sets of features: conventional NetFlow variables and distributional features based on NetFlow variables. In addition to using static summaries of NetFlow features, we use quantiles of their IP-level distributions as input features in predictive models to predict whether an IP belongs to known botnet families. These models are used to develop intrusion detection systems to predict traffic traces identified with malicious attacks. The results are validated by matching predictions to existing denylists of published malicious IP addresses and deep packet inspection. The usage of our proposed novel distributional features, combined with techniques that enable modelling complex input feature spaces result in highly accurate predictions by our trained models.

Past research on grammar induction has found promising results in predicting parts-of-speech from n-grams using a fixed vocabulary and a fixed context. In this study, we investigated grammar induction whereby we varied vocabulary size and context size. Results indicated that as context increased for a fixed vocabulary, overall accuracy initially increased but then leveled off. Importantly, this increase in accuracy did not occur at the same rate across all syntactic categories. We also address the dynamic relation between context and vocabulary in terms of grammar induction in an unsupervised methodology. We formulate a model that represents a relationship between vocabulary and context for grammar induction. Our results concur with what has been called the word spurt phenomenon in the child language acquisition literature.