Independent Component Analysis (ICA) plays a central role in modern machine learning as a flexible framework for feature extraction. We introduce a horseshoe-type prior with a latent Polya-Gamma scale mixture representation, yielding scalable algorithms for both point estimation via expectation-maximization (EM) and full posterior inference via Markov chain Monte Carlo (MCMC). This hierarchical formulation unifies several previously disparate estimation strategies within a single Bayesian framework. We also establish the first theoretical guarantees for hierarchical Bayesian ICA, including posterior contraction and local asymptotic normality results for the unmixing matrix. Comprehensive simulation studies demonstrate that our methods perform competitively with widely used ICA tools. We further discuss implementation of conditional posteriors, envelope-based optimization, and possible extensions to flow-based architectures for nonlinear feature extraction and deep learning. Finally, we outline several promising directions for future work.

翻译：独立成分分析（ICA）作为特征提取的灵活框架，在现代机器学习中占据核心地位。本文引入了一种具有潜在Polya-Gamma尺度混合表示的马蹄型先验，通过期望最大化（EM）实现点估计，并通过马尔可夫链蒙特卡洛（MCMC）实现全后验推断，从而得到可扩展的算法。这种分层表述将先前几种分散的估计策略统一在单一的贝叶斯框架内。我们还首次为分层贝叶斯ICA建立了理论保证，包括解混矩阵的后验收缩性和局部渐近正态性结果。全面的仿真研究表明，我们的方法与广泛使用的ICA工具相比具有竞争力。我们进一步讨论了条件后验的实现、基于包络的优化，以及向基于流的架构扩展的可能性，以用于非线性特征提取和深度学习。最后，我们概述了未来工作的几个有前景的方向。