Institute of Genetics and Biotechnology, Faculty of Agricultural Sciences, Aarhus University, Aarhus, Denmark.
BMC Bioinformatics. 2010 Jan 11;11:18. doi: 10.1186/1471-2105-11-18.
Chow and Liu showed that the maximum likelihood tree for multivariate discrete distributions may be found using a maximum weight spanning tree algorithm, for example Kruskal's algorithm. The efficiency of the algorithm makes it tractable for high-dimensional problems.
We extend Chow and Liu's approach in two ways: first, to find the forest optimizing a penalized likelihood criterion, for example AIC or BIC, and second, to handle data with both discrete and Gaussian variables. We apply the approach to three datasets: two from gene expression studies and the third from a genetics of gene expression study. The minimal BIC forest supplements a conventional analysis of differential expression by providing a tentative network for the differentially expressed genes. In the genetics of gene expression context the method identifies a network approximating the joint distribution of the DNA markers and the gene expression levels.
The approach is generally useful as a preliminary step towards understanding the overall dependence structure of high-dimensional discrete and/or continuous data. Trees and forests are unrealistically simple models for biological systems, but can provide useful insights. Uses include the following: identification of distinct connected components, which can be analysed separately (dimension reduction); identification of neighbourhoods for more detailed analyses; as initial models for search algorithms with a larger search space, for example decomposable models or Bayesian networks; and identification of interesting features, such as hub nodes.
Chow 和 Liu 表明，对于多元离散分布，可以使用最大权重生成树算法（例如 Kruskal 算法）找到最大似然树。该算法的效率使其适用于高维问题。
我们以两种方式扩展了 Chow 和 Liu 的方法：首先，找到优化惩罚似然准则（例如 AIC 或 BIC）的森林，其次，处理同时具有离散和高斯变量的数据。我们将该方法应用于三个数据集：两个来自基因表达研究，第三个来自基因表达遗传学研究。最小 BIC 森林通过为差异表达基因提供一个暂定网络，补充了传统的差异表达分析。在基因表达遗传学背景下，该方法识别出一个近似于 DNA 标记和基因表达水平联合分布的网络。
该方法通常可作为理解高维离散和/或连续数据整体依赖结构的初步步骤。树和森林对于生物系统来说是不切实际的简单模型，但可以提供有用的见解。用途包括以下几个方面：识别不同的连接组件，可以分别进行分析（降维）；识别更详细分析的邻域；作为更大搜索空间的搜索算法的初始模型，例如可分解模型或贝叶斯网络；以及识别有趣的特征，如枢纽节点。
