Bayesian alignment using hierarchical models, with applications in protein bioinformatics
基于层级模型的贝叶斯配准及其蛋白质生物信息学应用AI 解读 ↓
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基于层级模型的贝叶斯配准及其蛋白质生物信息学应用
- 研究问题
- 当空间点集未标记、仅部分标记或存在未匹配点时，如何同时推断点之间的对应关系与仿射或刚体几何变换？
- 方法与思路
- 作者以潜在真实点位置的泊松过程构建层级贝叶斯模型，结合 EM 与马尔可夫链蒙特卡洛，并为未知旋转采用条件共轭设定。
- 材料陈述的贡献
- 摘要称模型简化计算并容纳部分标记信息，在一类损失下最优匹配点估计仅依赖一个参数，并展示二维与三维蛋白质配准。
- 阅读关注点
- 阅读全文时应核对泊松过程与观测模型、变换和匹配的可识别性、损失函数族，以及旋转先验、算法诊断和部分标记的使用。
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原文摘要
An important problem in shape analysis is to match configurations of points in space after 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 hierarchical model is based on a Poisson process for hidden true point locations; this leads to considerable mathematical simplification and efficiency of implementation of EM and Markov chain Monte Carlo algorithms. We find a novel use for classical 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 two dimensions, and the second consists of aligning active sites of proteins in three dimensions. In the latter case, we also use information related to the grouping of the amino acids, as an example of a more general capability of our methodology to include partial labelling information. We discuss some open problems and suggest directions for future work.