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Proactive cyber-risk assessment is gaining momentum due to the wide range of sectors that can benefit from the prevention of cyber-incidents by preserving integrity, confidentiality, and the availability of data. The rising attention to cybersecurity also results from the increasing connectivity of cyber-physical systems, which generates multiple sources of uncertainty about emerging cyber-vulnerabilities. This work introduces a robust statistical framework for quantitative and qualitative reasoning under uncertainty about cyber-vulnerabilities and their prioritisation. Specifically, we take advantage of mid-quantile regression to deal with ordinal risk assessments, and we compare it to current alternatives for cyber-risk ranking and graded responses. For this purpose, we identify a novel accuracy measure suited for rank invariance under partial knowledge of the whole set of existing vulnerabilities. The model is tested on both simulated and real data from selected databases that support the evaluation, exploitation, or response to cyber-vulnerabilities in realistic contexts. Such datasets allow us to compare multiple models and accuracy measures, discussing the implications of partial knowledge about cyber-vulnerabilities on threat intelligence and decision-making in operational scenarios., Comment: 37 pages, 21 figures. Comments are welcome!

We propose a new method to combine adaptive processes with a class of entropy estimators for the case of streams of data. Starting from a first estimation obtained from a batch of initial data, model parameters are estimated at each step by combining the prior knowledge with the new observation (or a block of observations). This allows to extend the maximum entropy technique to a dynamical setting, also distinguishing between entropic contributions of the signal and the error. Furthermore, it provides a suitable approximation of standard GME problems when the exacted solutions are hard to evaluate. We test this method by performing numerical simulations at various sample sizes and batch dimensions. Moreover, we extend this analysis exploring intermediate cases between streaming GCE and standard GCE, i.e. considering blocks of observations of different sizes to update the estimates, and incorporating collinearity effects as well. The role of time in the balance between entropic contributions of signal and errors is further explored considering a variation of the Streaming GCE algorithm, namely, Weighted Streaming GCE. Finally, we discuss the results: in particular, we highlight the main characteristics of this method, the range of application, and future perspectives., Comment: 22 pages, 11 figures