Summary:
As Machine Learning models are considered for autonomous decisions with significant social impact, the need to understand how these models work rises rapidly. Explainable Artificial Intelligence (XAI) aims to provide interpretations for predictions made by Machine Learning models, in order to make the model trustworthy and more transparent for the user. For example, selecting relevant input variables for the problem directly impacts the model’s ability to learn and make accurate predictions. One of the main XAI techniques to obtain input variable importance is the sensitivity analysis based on partial derivatives. However, existing literature of this method provides no justification of the aggregation metrics used to retrieved information from the partial derivatives. In this paper, a theoretical framework is proposed to study sensitivities of ML models using metric techniques. From this metric interpretation, a complete family of new quantitative metrics called α-curves is extracted. These α-curves provide information with greater depth on the importance of the input variables for a machine learning model than existing XAI methods in the literature. We demonstrate the effectiveness of the α-curves using synthetic and real datasets, comparing the results against other XAI methods for variable importance and validating the analysis results with the ground truth or literature information.
Spanish layman's summary:
Las α-curvas muestran la importancia de una característica al pasar del “efecto promedio” (α = 1) al “caso singular” (α → ∞) al agregar sus sensibilidades puntuales mediante una media generalizada. La forma de la curva indica si la característica se comporta de forma lineal en todas partes (curva plana) o tiene regiones de alto impacto (incremento pronunciado). En los experimentos, las α-curvas detectan las variables más importantes tanto de manera global como local en una importancia unificada.
English layman's summary:
α-curves plot a feature’s importance as you move from “average effect” (α=1) to “worst-case spike” (α→∞) by aggregating its pointwise sensitivities with a generalized mean. The non-decreasing curve’s shape tells if a feature acts linearly everywhere (flat curve) or has high-impact regions (steep rise). In experiments, α-curves recover known global drivers and uncover hidden local hotspots.
Keywords: Sensitivity; Machine learning; Feature importance; Explainable A; Regressio; Feature engineering; Neural networks
JCR-JIF Impact Factor and WoS quartile: 7,800 - Q1 (2025)
DOI reference:
https://doi.org/10.1016/j.asoc.2025.113300
Published on paper: August 2025.
Published on-line: May 2025.
Citation:
J. Pizarroso, D. Alfaya, J. Portela, A. Muñoz, "Metric tools for sensitivity analysis with applications to neural networks", Applied Soft Computing, Vol. 180, pp. 113300, August 2025. [Online: May 2025] doi: 10.1016/j.asoc.2025.113300
