Xinying Liu

Mudi Jiang, Jiahui Zhou, Xinying Liu et al.

Fair clustering has gained increasing attention in recent years, especially in applications involving socially sensitive attributes. However, existing fair clustering methods often lack interpretability, limiting their applicability in high-stakes scenarios where understanding the rationale behind clustering decisions is essential. In this work, we address this limitation by proposing an interpretable and fair clustering framework, which integrates fairness constraints into the structure of decision trees. Our approach constructs interpretable decision trees that partition the data while ensuring fair treatment across protected groups. To further enhance the practicality of our framework, we also introduce a variant that requires no fairness hyperparameter tuning, achieved through post-pruning a tree constructed without fairness constraints. Extensive experiments on both real-world and synthetic datasets demonstrate that our method not only delivers competitive clustering performance and improved fairness, but also offers additional advantages such as interpretability and the ability to handle multiple sensitive attributes. These strengths enable our method to perform robustly under complex fairness constraints, opening new possibilities for equitable and transparent clustering.

Xinying Liu, Lianyu Hu, Mudi Jiang et al.

Cluster analysis is a fundamental research issue in statistics and machine learning. In many modern clustering methods, we need to determine whether two subsets of samples come from the same cluster. Since these subsets are usually generated by certain clustering procedures, the deployment of classic two-sample tests in this context would yield extremely smaller p-values, leading to inflated Type-I error rate. To overcome this bias, we formally introduce the two-cluster test issue and argue that it is a totally different significance testing issue from conventional two-sample test. Meanwhile, we present a new method based on the boundary points between two subsets to derive an analytical p-value for the purpose of significance quantification. Experiments on both synthetic and real data sets show that the proposed test is able to significantly reduce the Type-I error rate, in comparison with several classic two-sample testing methods. More importantly, the practical usage of such two-cluster test is further verified through its applications in tree-based interpretable clustering and significance-based hierarchical clustering.

Zengyou He, Zerun Li, Junjie Dong et al.

In this paper, we present a new classifier, which integrates significance testing results over different random subspaces to yield consensus p-values for quantifying the uncertainty of classification decision. The null hypothesis is that the test sample has no association with the target class on a randomly chosen subspace, and hence the classification problem can be formulated as a problem of testing for the conjunction of hypotheses. The proposed classifier can be easily deployed for the purpose of conformal prediction and selective classification with reject and refine options by simply thresholding the consensus p-values. The theoretical analysis on the generalization error bound of the proposed classifier is provided and empirical studies on real data sets are conducted as well to demonstrate its effectiveness.