摘要翻译：
具有潜在结构的统计模型的历史可以追溯到20世纪50年代，并在社会科学中得到了广泛的应用，最近在计算生物学和机器学习中得到了广泛的应用。本文研究了社会学家Paul F.Lazarfeld最初为范畴变量提出的基本潜类模型，并解释了它的几何结构。我们将潜在类模型的统计性质和几何性质进行了比较，并从几何角度说明了与极大似然估计和相关统计推断相关的许多问题的原因。特别地，我们重点讨论了模型维数的不可识别性和确定、似然函数的最大化以及对称数据的影响等问题。我们用各种不同维度和复杂度的合成和现实生活的表格来说明这些现象。这项工作的大部分动机源于我们详细介绍和描述的“100瑞士法郎”问题。
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英文标题：
《Maximum Likelihood Estimation in Latent Class Models For Contingency
  Table Data》
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作者：
S.E. Fienberg, P. Hersh, A. Rinaldo and Y. Zhou
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Statistical models with latent structure have a history going back to the 1950s and have seen widespread use in the social sciences and, more recently, in computational biology and in machine learning. Here we study the basic latent class model proposed originally by the sociologist Paul F. Lazarfeld for categorical variables, and we explain its geometric structure. We draw parallels between the statistical and geometric properties of latent class models and we illustrate geometrically the causes of many problems associated with maximum likelihood estimation and related statistical inference. In particular, we focus on issues of non-identifiability and determination of the model dimension, of maximization of the likelihood function and on the effect of symmetric data. We illustrate these phenomena with a variety of synthetic and real-life tables, of different dimension and complexity. Much of the motivation for this work stems from the "100 Swiss Francs" problem, which we introduce and describe in detail.
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PDF链接：
https://arxiv.org/pdf/709.3535