Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for
understanding uncertainty and structure in matrix data. However, a large volume
of applied work optimizes traditional non-Bayesian NMF objectives that fail to
provide a principled understanding of the non-identifiability inherent in NMF--
an issue ideally addressed by a Bayesian approach. Despite their suitability,
current Bayesian NMF approaches have failed to gain popularity in an applied
setting; they sacrifice flexibility in modeling for tractable computation, tend
to get stuck in local modes, and require many thousands of samples for
meaningful uncertainty estimates. We address these issues through a
particle-based variational approach to Bayesian NMF that only requires the
joint likelihood to be differentiable for tractability, uses a novel
initialization technique to identify multiple modes in the posterior, and
allows domain experts to inspect a `small' set of factorizations that
faithfully represent the posterior. We introduce and employ a class of
likelihood and prior distributions for NMF that formulate a Bayesian model
using popular non-Bayesian NMF objectives. On several real datasets, we obtain
better particle approximations to the Bayesian NMF posterior in less time than
baselines and demonstrate the significant role that multimodality plays in
NMF-related tasks.

使用粒子变分贝叶斯方法处理非负矩阵分解中的非识别性问题，提高贝叶斯 NMF 后验分布的精度并发现多模态的重要作用。