论文标题
用于二进制数据的球形因素分析的贝叶斯方法
A Bayesian Approach to Spherical Factor Analysis for Binary Data
论文作者
论文摘要
因子模型被广泛用于不同的应用领域，用于包括降低维度，协方差估计和功能工程的目的。传统因子模型可以看作是线性嵌入方法的实例，该方法将多元观测值投射到较低维的欧几里得潜在空间上。本文讨论了用于多元二进制数据的新的几何嵌入模型，其中嵌入空间对应于球形歧管，并具有潜在的未知维度。最终的模型将传统因子模型作为特殊情况，但提供了额外的灵活性。此外，与几何嵌入的其他技术不同，模型易于解释，并且可以正确量化与潜在特征相关的不确定性。使用模拟研究和有关美国参议院投票记录的真实数据来说明这些优势。
Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding methods that project multivariate observations onto a lower dimensional Euclidean latent space. This paper discusses a new class of geometric embedding models for multivariate binary data in which the embedding space correspond to a spherical manifold, with potentially unknown dimension. The resulting models include traditional factor models as a special case, but provide additional flexibility. Furthermore, unlike other techniques for geometric embedding, the models are easy to interpret, and the uncertainty associated with the latent features can be properly quantified. These advantages are illustrated using both simulation studies and real data on voting records from the U.S. Senate.
