Contingency Space: A Semimetric Space for Classification Evaluation

In Machine Learning, a supervised model's performance is measured using the evaluation metrics. In this study, we first present our motivation by revisiting the major limitations of these metrics, namely one-dimensionality, lack of context, lack of intuitiveness, uncomparability, binary restriction, and uncustomizability of metrics. In response, we propose Contingency Space, a bounded semimetric space that provides a generic representation for any performance evaluation metric. Then we showcase how this space addresses the limitations. In this space, each metric forms a surface using which we visually compare different evaluation metrics. Taking advantage of the fact that a metric's surface warps proportionally to the degree of which it is sensitive to the class-imbalance ratio of data, we introduce Imbalance Sensitivity that quantifies the skew-sensitivity. Since an arbitrary model is represented in this space by a single point, we introduce Learning Path for qualitative and quantitative analyses of the training process. Using the semimetric that contingency space is endowed with, we introduce Tau as a new cost sensitive and Imbalance Agnostic metric. Lastly, we show that contingency space addresses multi-class problems as well. Throughout this work, we define each concept through stipulated definitions and present every application with practical examples and visualizations.