Methods for analysis of principal components in discrete data have existed
for some time under various names such as grade of membership modelling,
probabilistic latent semantic analysis, and genotype inference with admixture.
In this paper we explore a number of extensions to the common theory, and
present some application of these methods to some common statistical tasks. We
show that these methods can be interpreted as a discrete version of ICA. We
develop a hierarchical version yielding components at different levels of
detail, and additional techniques for Gibbs sampling. We compare the algorithms
on a text prediction task using support vector machines, and to information
retrieval.

本文介绍了一些扩展方法，并应用到常见的统计任务中，将其解释为离散版 ICA，通过支持向量机与信息检索进行文本预测任务的算法比较。

应用离散 PCA 进行数据分析

Applying Discrete PCA in Data Analysis

We develop the relational topic model (RTM), a hierarchical model of both
network structure and node attributes. We focus on document networks, where the
attributes of each document are its words, that is, discrete observations taken
from a fixed vocabulary. For each pair of documents, the RTM models their link
as a binary random variable that is conditioned on their contents. The model
can be used to summarize a network of documents, predict links between them,
and predict words within them. We derive efficient inference and estimation
algorithms based on variational methods that take advantage of sparsity and
scale with the number of links. We evaluate the predictive performance of the
RTM for large networks of scientific abstracts, web documents, and
geographically tagged news.

本文提出了一种关系主题模型，可以用于文档网络的摘要、链接预测和内部词汇预测等方面，并基于变分方法构建了高效的推断和估计算法。

文档网络的分层关系模型

Hierarchical relational models for document networks

We propose a nonparametric Bayesian factor regression model that accounts for
uncertainty in the number of factors, and the relationship between factors. To
accomplish this, we propose a sparse variant of the Indian Buffet Process and
couple this with a hierarchical model over factors, based on Kingman's
coalescent. We apply this model to two problems (factor analysis and factor
regression) in gene-expression data analysis.

提出一种非参数贝叶斯因子回归模型，考虑因子个数的不确定性和因子间的关系，通过 Kingman coalescent 基于因子的分层模型，将其与 sparse Indian Buffet Process 相结合，应用于基因表达数据分析中的因子分析和因子回归问题。