Game-theoretic extensions of logistic regression

Logistic regression (LR) is a widely used and well-established tool for classification tasks, valued for its simplicity and interpretability. However, its reliance on linear separators transformed by a sigmoid function limits its flexibility, particularly when dealing with non-linear decision boundaries. To address this limitation, Tehrani et al. proposed an extension of LR where the linear separator is replaced by a piecewise-linear known as Choquet integral. While effective, this approach, known as “Choquistic regression”, faces the curse of dimensionality, as its parameter count grows exponentially with the number of input features. To mitigate this issue, simplified variants of the Choquet integral, such as the 2-additive Choquet integral, have been proposed. These variants restrict interactions to at most two features, significantly reducing complexity while delivering competitive performance compared to unrestricted models. However, the monotonicity constraints imposed by the Choquistic approach remain a limitation, reducing its applicability to real-world scenarios. In this paper, we propose a novel formulation of logistic regression that integrates the Choquet integral, with parameters defined through a cooperative game framework. Additionally, we explore game-based aggregation functions such as the multilinear model, which also captures feature interactions effectively. To overcome the curse of dimensionality, we utilize 2-additive games, which significantly reduce the number of parameters while preserving competitive accuracy. This reduction in complexity is empirically validated through a comparative study of restricted and unrestricted logistic regression variants on a COVID-19 dataset. Furthermore, the results highlight the interpretability advantages of these models, demonstrating their practical value in real-world applications.