线性潜结构分析：带线性约束的混合分布模型
Linear Latent Structure Analysis: Mixture Distribution Models with Linear Constraints
摘要：
提出了一种分析高维分类数据的新方法--线性潜结构分析。LLS模型属于隐结构模型族，是一种受局部独立性约束的混合分布模型。LLS分析将一类混合分布视为线性空间，通过对混合分布施加线性约束得到LLS模型。LLS模型在适度条件下是可识别的，并且是一致可估计的。LLS分析的一个显著特点是存在高性能的数值算法，它将参数估计简化为一系列线性代数问题。初步的仿真实验表明，该算法的原型模型参数的恢复质量良好。
英文摘要：
A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the local independence assumption. LLS analysis explicitly considers a family of mixed distributions as a linear space and LLS models are obtained by imposing linear constraints on the mixing distribution. LLS models are identifiable under modest conditions and are consistently estimable. A remarkable feature of LLS analysis is the existence of a high-performance numerical algorithm, which reduces parameter estimation to a sequence of linear algebra problems. Preliminary simulation experiments with a prototype of the algorithm demonstrated a good quality of restoration of model parameters.
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