发表机构
University of Padova; University of Edinburgh; WU Wien（帕多瓦大学; 爱丁堡大学; 维也纳经济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出广义下三角过程先验，用于因子模型中的因子数量和稀疏结构学习，通过Gibbs采样实现后验计算，并在模拟和大五人格数据上验证有效性。
AI 中文摘要
在多变量数据分析中，因子模型是一种强大的技术，既能降低维度，又能促进对控制观测数据的潜在决定因素的定性理解。然而，由于旋转不变性，因子载荷矩阵的不可识别性常常阻碍可解释性。解决此问题的一种主流策略是考虑正下三角结构。最近文献中提出了对后一条件的放宽，即所谓的广义下三角结构。然而，其贝叶斯实现面临重大挑战，需要复杂的可逆跳跃算法，并且由于模型参数的可解释性有限，先验设定变得困难。在本文中，我们引入了一种广义下三角过程先验，它允许全局和组件内稀疏结构，以学习因子数量以及观测向量内可能的稀疏结构。所提出的方法通过利用关于秩和稀疏特征的可能不同的先验信息，提供了直接的先验参数设定。我们还探讨了与印度自助餐过程的联系，进一步深入了解所提出先验诱导的稀疏结构。后验计算可以通过带有Metropolis-Hastings移动的Gibbs采样器进行。通过综合模拟和对大五人格测试数据的分析，证明了所提出方法的有效性。
英文摘要
In the analysis of multivariate data, factor models represent a powerful technique for both reducing dimensionality and facilitating qualitative understanding of the latent determinants governing the observed data. Interpretability, however, is often hindered by the non-identifiability of factor loading matrices due to rotational invariance. A prevailing strategy to address this issue is to consider positive lower triangular structures. A relaxation of the latter condition has been recently proposed in the literature with the so called generalized lower triangular structure. However, its Bayesian implementation presents substantial challenges, requiring complex reversible-jump algorithms and making prior elicitation difficult because of the limited interpretability of the model parameters. In this paper, we introduce a generalized lower triangular process prior that allows both global and within-component sparsity structures for learning both the number of factors and possible sparsity structures within the vector of observations. The proposed approach provides straightforward prior parameters elicitation exploiting possibly different prior information on the rank and sparsity characteristics. We also explore connections with the Indian buffet process, providing further insight into the sparsity structure induced by the proposed prior. Posterior computation can be performed resorting to a Gibbs sampler with Metropolis-Hastings moves. The efficacy of the proposed method is demonstrated through comprehensive simulations and the analysis of the Big Five Personality Test data.
