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Expected Probabilistic Hierarchies

Overview of our proposed EPH model. During training, EPH first samples discrete hierarchies using our differentiable hierarchy sampling and a subgraph using our subgraph sampling procedure. The expected scores are then computed and averaged. Finally, the probabilistic hierarchy is updated via backpropagation.

Abstract

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 on quantitative results and provides meaningful hierarchies in qualitative evaluations.

Links

Cite

@inproceedings{kollovieh2024eph,
    title = {Expected Probabilistic Hierarchies},
    author = {Kollovieh, Marcel and Charpentier, Bertrand and Z\"ugner, Daniel and G\"unnemann, Stephan},
    journal={Advances in Neural Information Processing Systems},
    volume={37},
    year = {2024},
}

 

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Informatik 26 - Data Analytics and Machine Learning


Prof. Dr. Stephan Günnemann

Technische Universität München
TUM School of Computation, Information and Technology
Department of Computer Science
Boltzmannstr. 3
85748 Garching 

Sekretariat:
Raum 00.11.057
Tel.: +49 89 289-17256
Fax: +49 89 289-17257

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