Explainable Clustering of Mixture Models

תקציר מקורי באנגליתarXiv:2411.01576v3 Announce Type: replace Abstract: The explainable clustering problem was first posed by Moshkovitz et al. (ICML 2020) and studies how well an axis-aligned decision tree with $K$ leaves can approximate a given clustering. The performance of the tree is measured via the \textit{price of explainability}, defined as the ratio between the clustering cost of the tree (where every leaf is a cluster) and the optimal cost. Several recent works have given worst-case characterizations of the price of explainability for different cost functions. However, these guarantees are data-agnostic and therefore notoriously pessimistic in practical clustering settings. In this paper, we study explainable clustering from the point of view of mixture models, which allows us to give the first dat