使用分层模型的贝叶斯比对及其在蛋白质生物信息学中的应用
Bayesian alignment using hierarchical models, with applications in protein bioinformatics
摘要：
形状分析中的一个重要问题是滤除几何变换后的空间点的构形匹配。在本文中，我们介绍了这样的任务，其中的配置中的点是未标记的，或最多有一个部分标签约束的匹配，并在其中一些点可能只出现在一个配置的层次模型。我们推导出程序的同时推理的匹配和转换，使用贝叶斯方法。我们的模型是基于一个泊松过程隐藏的真实点的位置，这导致了相当大的数学简化和效率的实现。我们发现了一个新的使用经典的分布，从方向统计在条件共轭规范的情况下，几何变换包括一个未知的旋转。在整个过程中，我们专注于仿射或刚性运动变换的情况。在广义参数损失函数族下，可以构造匹配矩阵的最优贝叶斯点估计，该估计仅依赖于该族中的单个参数。我们的方法说明了从生物信息学的两个应用程序。第一个问题是在2维中匹配蛋白质凝胶，第二个问题是在3维中对齐蛋白质的活性位点。在后一种情况下，我们还使用与氨基酸分组相关的信息。我们讨论了一些开放的问题，并提出了未来工作的方向。
英文摘要：
An important problem in shape analysis is to match configurations of points in space filtering out some geometrical transformation. In this paper we introduce hierarchical models for such tasks, in which the points in the configurations are either unlabelled, or have at most a partial labelling constraining the matching, and in which some points may only appear in one of the configurations. We derive procedures for simultaneous inference about the matching and the transformation, using a Bayesian approach. Our model is based on a Poisson process for hidden true point locations; this leads to considerable mathematical simplification and efficiency of implementation. We find a novel use for classic distributions from directional statistics in a conditionally conjugate specification for the case where the geometrical transformation includes an unknown rotation. Throughout, we focus on the case of affine or rigid motion transformations. Under a broad parametric family of loss functions, an optimal Bayesian point estimate of the matching matrix can be constructed, that depends only on a single parameter of the family. Our methods are illustrated by two applications from bioinformatics. The first problem is of matching protein gels in 2 dimensions, and the second consists of aligning active sites of proteins in 3 dimensions. In the latter case, we also use information related to the grouping of the amino acids. We discuss some open problems and suggest directions for future work.
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