Stéphane Mussard

Cassandra Mussard, Stéphane Mussard

The Gini Multidimensional Scaling (Gini MDS) framework extends the Euclidean multidimensional scaling. We introduce a Gini pseudo-distance based on values and their ranks that depends on a fine-tunable hyperparameter. This pseudo-distance allows flexible exploration of latent configurations, enabling embeddings that best match observed dissimilarities. The Gini MDS is shown to be robust to noise and outliers, making it well-suited for real-world applications. We provide experiments on 16 UCI datasets with outliers and on MNIST images with noise to show that the Gini MDS outperforms the Euclidean MDS on noisy data. Finally, a tensor-based implementation in \texttt{PyTorch} provides GPU acceleration and efficient computation compared to the standard MDS of the \texttt{sklearn} library.

Adam Belahcen, Stéphane Mussard

We introduce Aumann-SHAP, an interaction-aware framework that decomposes counterfactual transitions by restricting the model to a local hypercube connecting baseline and counterfactual features. Each hyper-cube is decomposed into a grid in order to construct an induced micro-player cooperative game in which elementary grid-step moves become players. Shapley and LES values on this TU-micro-game yield: (i) within-pot contribution of each feature to the interaction with other features (interaction explainability), and (ii) the contribution of each instance and each feature to the counterfactual analysis (individual and global explainability). In particular, Aumann-LES values produce individual and global explanations along the counterfactual transition. Shapley and LES values converge to the diagonal Aumann-Shapley (integrated-gradients) attribution method. Experiments on the German Credit dataset and MNIST data show that Aumann-LES produces robust results and better explanations than the standard Shapley value during the counterfactual transition.

Fadoua Amri-Jouidel, Emmanuel Kemel, Stéphane Mussard

Explainability and fairness have mainly been considered separately, with recent exceptions trying the explain the sources of unfairness. This paper shows that the Shapley value can be used to both define and explain unfairness, under standard group fairness criteria. This offers an integrated framework to estimate and derive inference on unfairness as-well-as the features that contribute to it. Our framework can also be extended from Shapley values to the family of Efficient-Symmetric-Linear (ESL) values, some of which offer more robust definitions of fairness, and shorter computation times. An illustration is run on the Census Income dataset from the UCI Machine Learning Repository. Our approach shows that ``Age", ``Number of hours" and ``Marital status" generate gender unfairness, using shorter computation time than traditional Bootstrap tests.

Cassandra Mussard, Arthur Charpentier, Stéphane Mussard

This paper introduces enhancements to the K-means and K-nearest neighbors (KNN) algorithms based on the concept of Gini prametric spaces, instead of traditional metric spaces. Unlike standard distance metrics, Gini prametrics incorporate both value-based and rank-based measures, offering robustness to noise and outliers. The main contributions include: (1) a Gini prametric that captures rank information alongside value distances; (2) a Gini K-means algorithm that is provably convergent and resilient to noisy data; and (3) a Gini KNN method that performs competitively with state-of-the-art approaches like Hassanat's distance in noisy environments. Experimental evaluations on 16 UCI datasets demonstrate the superior performance and efficiency of the Gini-based algorithms in clustering and classification tasks. This work opens new directions for rank-based prametrics in machine learning and statistical analysis.