Expected Probabilistic Hierarchies

Hierarchical clustering has usually been addressed by discrete optimization using heuristics or continuous optimization of relaxed scores for hierarchies. In this work, we propose to optimize expected scores under a probabilistic model over hierarchies. (1) We show theoretically that the global optimal values of the expected Dasgupta cost and Tree-Sampling divergence (TSD), two unsupervised metrics for hierarchical clustering, are equal to the optimal values of their discrete counterparts contrary to some relaxed scores. (2) We propose Expected Probabilistic Hierarchies (EPH), a probabilistic model to learn hierarchies in data by optimizing expected scores. EPH uses differentiable hierarchy sampling enabling end-to-end gradient descent based optimization, and an unbiased subgraph sampling approach to scale to large datasets. (3) We evaluate EPH on synthetic and real-world datasets including vector and graph datasets. EPH outperforms all other approaches quantitatively and provides meaningful hierarchies in qualitative evaluations.