Defining the number of latent factors has been one of the most challenging problems in factor analysis. Infinite factor models offer a solution to this problem by applying increasing shrinkage on the columns of factor loading matrices, thus penalising increasing factor dimensionality. The adaptive MCMC algorithms used for inference in such models allow to defer the dimension of the latent factor space automatically based on the data. This paper presents an overview of Bayesian models for infinite factorisations with some discussion on the properties of such models as well as their comparative advantages and drawbacks.

翻译：在因子分析中，确定潜在因子数量一直是最具挑战性的问题之一。无限因子模型通过对因子载荷矩阵的列施加递增的收缩效应，从而对因子维度的增加进行惩罚，进而解决了这一问题。用于此类模型推论的适应性马尔可夫链蒙特卡洛算法能够根据数据自动延迟潜在因子空间的维度确定。本文综述了面向无限因子分解的贝叶斯模型，讨论了此类模型的性质及其相对优势与局限。