Bayesian Tree-Dependent Factorization

ICLR 2025 Conference Submission12601 Authors

Keywords: factorization, Bayesian models, multi-view, hierarchical, gene expression, clinical

TL;DR: We propose a highly interpretable Bayesian hierarchical factorization model, then apply a multi-view formulation to breast cancer patient data.

Abstract: We propose Bayesian Tree-Dependent Factorization (BTF), a novel probabilistic representation learning model that uncovers hierarchical, continuous latent factors in complex datasets. BTF constructs a tree-based model that discovers interpretable factorizations of the data wherein each factor has a conditional relationship to its parent, allowing it to capture both global and local effects. This approach is particularly well-suited for biological data, where traditional methods like PCA fail to capture higher-order dependencies and hierarchical structure. A significant contribution of this work is the multi-view extension of BTF, which allows for the joint analysis of multiple data modalities. By learning shared loadings across views while maintaining distinct factors for each modality, multi-view BTF improves performance and enables deeper insights into the relationships between different data types. We demonstrate the performance of BTF in simulations as well as in a real-world application to gene expression and clinical data in breast cancer patients, revealing biologically and clinically meaningful patient trends, and showing that BTF is a valuable representation learning tool for analysis and hypothesis generation.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 12601