Bayesian Pyramids: identifiable multilayer discrete latent structure models for discrete data
Bayesian Pyramids: identifiable multilayer discrete latent structure models for discrete data
复制标题
贝叶斯金字塔：离散数据的可识别多层离散潜在结构模型
DOI：
10.1093/jrsssb/qkad010
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Dunson, David B
中科院分区：
文献类型：
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作者：
Gu, Yuqi;Dunson, David B
高维分类数据通常在生物医学和社会科学中收集。构建可解释的简约模型来执行降维并从此类离散数据中发现有意义的潜在结构非常重要。可识别性是此类场景中有效建模和推理的基本要求，但当存在复杂的潜在结构时，解决起来却充满挑战。在本文中，我们提出了一类用于离散数据的可识别的多层（可能很深）离散潜在结构模型，称为贝叶斯金字塔。我们通过在金字塔形深层潜在有向图上开发新颖的透明条件来建立贝叶斯金字塔的可识别性。所提出的可识别性条件可以确保适当先验下的贝叶斯后验一致性。作为说明，我们考虑两个潜在层模型并提出贝叶斯收缩估计方法。该模型的仿真结果证实了模型参数的可识别性和可估计性。该方法应用于 DNA 核苷酸序列数据揭示了有用的离散潜在特征，这些特征可以高度预测序列类型。所提出的框架为离散数据的可解释无监督学习提供了一种方法，并且可以成为流行机器学习方法的有用替代方案。
High-dimensional categorical data are routinely collected in biomedical and social sciences. It is of great importance to build interpretable parsimonious models that perform dimension reduction and uncover meaningful latent structures from such discrete data. Identifiability is a fundamental requirement for valid modeling and inference in such scenarios, yet is challenging to address when there are complex latent structures. In this article, we propose a class of identifiable multilayer (potentially deep) discrete latent structure models for discrete data, termedBayesian Pyramids. We establish the identifiability of Bayesian Pyramids by developing novel transparent conditions on the pyramid-shaped deep latent directed graph. The proposed identifiability conditions can ensure Bayesian posterior consistency under suitable priors. As an illustration, we consider the two-latent-layer model and propose a Bayesian shrinkage estimation approach. Simulation results for this model corroborate the identifiability and estimatability of model parameters. Applications of the methodology to DNA nucleotide sequence data uncover useful discrete latent features that are highly predictive of sequence types. The proposed framework provides a recipe for interpretable unsupervised learning of discrete data and can be a useful alternative to popular machine learning methods.