This thesis extends the partial response methodology to a range of non-linear black box models, such as Random Forests and Multi-Layer Perceptron neural networks. The outcome is a model-agnostic interpretability framework capable of maintaining the predictive power of the original black box models whilst offering full transparency into their decision-making processes. The proposed framework demonstrates competitive performance when evaluated against established interpretability techniques, both in terms of accuracy and explainability. The framework enables the construction of intuitive univariate and bivariate visualisations derived from the partial response functions. These visual tools effectively communicate how individual variables, or pairs of variables, influence predictions across their entire respective domains. By providing a detailed, range-wide view of the variables, these plots support more comprehensive insights into model behaviour and facilitate informed decision-making. In addition, preliminary experimentation is shown in the area of bootstrapping, wherein repeated resampling of the data was employed to assess the stability and reliability of the derived partial responses. This approach enhances the robustness of the interpretability outputs by incorporating measures of uncertainty, such as confidence intervals, thereby increasing user trust in the resulting explanations. All experimental analyses are conducted using a combination of synthetic datasets, designed to evaluate the methodology under controlled and interpretable conditions, and real-world datasets, which served to examine the framework’s efficacy in capturing complex, non-linear interactions among variables in noisy and heterogeneous environments. The use of both types of data ensures a comprehensive assessment of the method’s generalisability and practical utility.
B Walters (2026) studied this question.