Zack Ellerby

Zack Ellerby, Christian Wagner, Stephen Broomell

Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields. Traditional and ubiquitous response formats such as Likert and Visual Analogue Scales require condensation of responses into discrete point values - but sometimes a range of options may better represent the correct answer. In this paper, we propose an efficient interval-valued response mode, whereby responses are made by marking an ellipse along a continuous scale. We discuss its potential to capture and quantify valuable information that would be lost using conventional approaches, while preserving a high degree of response-efficiency. The information captured by the response interval may represent a possible response range - i.e., a conjunctive set, such as the real numbers between three and six. Alternatively, it may reflect uncertainty in respect to a distinct response - i.e., a disjunctive set, such as a confidence interval. We then report a validation study, utilizing our recently introduced open-source software (DECSYS) to explore how interval-valued survey responses reflect experimental manipulations of several factors hypothesised to influence interval width, across multiple contexts. Results consistently indicate that respondents used interval widths effectively, and subjective participant feedback was also positive. We present this as initial empirical evidence for the efficacy and value of interval-valued response capture. Interestingly, our results also provide insight into respondents' reasoning about the different aforementioned types of intervals - we replicate a tendency towards overconfidence for those representing epistemic uncertainty (i.e., disjunctive sets), but find intervals representing inherent range (i.e., conjunctive sets) to be well-calibrated.

Shaily Kabir, Christian Wagner, Zack Ellerby

Most of statistics and AI draw insights through modelling discord or variance between sources of information (i.e., inter-source uncertainty). Increasingly, however, research is focusing upon uncertainty arising at the level of individual measurements (i.e., within- or intra-source), such as for a given sensor output or human response. Here, adopting intervals rather than numbers as the fundamental data-type provides an efficient, powerful, yet challenging way forward -- offering systematic capture of uncertainty-at-source, increasing informational capacity, and ultimately potential for insight. Following recent progress in the capture of interval-valued data, including from human participants, conducting machine learning directly upon intervals is a crucial next step. This paper focuses on linear regression for interval-valued data as a recent growth area, providing an essential foundation for broader use of intervals in AI. We conduct an in-depth analysis of state-of-the-art methods, elucidating their behaviour, advantages, and pitfalls when applied to datasets with different properties. Specific emphasis is given to the challenge of preserving mathematical coherence -- i.e., ensuring that models maintain fundamental mathematical properties of intervals throughout -- and the paper puts forward extensions to an existing approach to guarantee this. Carefully designed experiments, using both synthetic and real-world data, are conducted -- with findings presented alongside novel visualizations for interval-valued regression outputs, designed to maximise model interpretability. Finally, the paper makes recommendations concerning method suitability for data sets with specific properties and highlights remaining challenges and important next steps for developing AI with the capacity to handle uncertainty-at-source.

Zack Ellerby, Josie McCulloch, Melanie Wilson et al.

Subjective judgements from experts provide essential information when assessing and modelling threats in respect to cyber-physical systems. For example, the vulnerability of individual system components can be described using multiple factors, such as complexity, technological maturity, and the availability of tools to aid an attack. Such information is useful for determining attack risk, but much of it is challenging to acquire automatically and instead must be collected through expert assessments. However, most experts inherently carry some degree of uncertainty in their assessments. For example, it is impossible to be certain precisely how many tools are available to aid an attack. Traditional methods of capturing subjective judgements through choices such as \emph{high}, \emph{medium} or \emph{low} do not enable experts to quantify their uncertainty. However, it is important to measure the range of uncertainty surrounding responses in order to appropriately inform system vulnerability analysis. We use a recently introduced interval-valued response-format to capture uncertainty in experts' judgements and employ inferential statistical approaches to analyse the data. We identify key attributes that contribute to hop vulnerability in cyber-systems and demonstrate the value of capturing the uncertainty around these attributes. We find that this uncertainty is not only predictive of uncertainty in the overall vulnerability of a given system component, but also significantly informs ratings of overall component vulnerability itself. We propose that these methods and associated insights can be employed in real world situations, including vulnerability assessments of cyber-physical systems, which are becoming increasingly complex and integrated into society, making them particularly susceptible to uncertainty in assessment.