RNA牛顿多面体与能量参数的可学习性
The RNA Newton Polytope and Learnability of Energy Parameters
摘要：
尽管人们对RNA二级结构和RNA-RNA相互作用的预测进行了近二十年的研究，但现有算法的准确性仍远不能令人满意。研究人员提出了越来越复杂的能量模型和改进的参数估计方法，期望赋予他们的方法足够的权力来解决这个问题。令人失望的是，产出只是略有改善，与预期不符。即使是最近的大规模特色机器学习方法也无法打破这一障碍。在本文中，我们引入了能量模型参数的可学习性的概念，作为其内在能力的度量。我们说能量模型的参数是可学习的，如果至少存在一组这样的参数，使每个已知的RNA结构都成为最小自由能结构。我们推导出了可学习性的必要条件，并给出了一个动态规划算法来评估它。我们的算法计算给定输入序列的集合中所有可行结构的特征向量的凸包。有趣的是，凸包与配分函数的牛顿多面体一致，作为能量参数的多项式。我们证明了我们的理论的应用，一个简单的能量模型组成的加权计数的A-U和C-G碱基对。我们的研究结果表明，这个简单的能量模型满足必要条件，从RNA STRAND v2.0数据库中选择的输入unpseudoknotted序列结构对的不到三分之一。对于另外三分之一，必要条件几乎没有被违反，这表明用更多的特征（如特纳环）来增强这个简单的能量模型可能会解决这个问题。8%的人严重违反了必要条件，这提供了一小部分需要进一步调查的困难情况。
英文摘要：
Despite nearly two scores of research on RNA secondary structure and RNA-RNA interaction prediction, the accuracy of the state-of-the-art algorithms are still far from satisfactory. Researchers have proposed increasingly complex energy models and improved parameter estimation methods in anticipation of endowing their methods with enough power to solve the problem. The output has disappointingly been only modest improvements, not matching the expectations. Even recent massively featured machine learning approaches were not able to break the barrier. In this paper, we introduce the notion of learnability of the parameters of an energy model as a measure of its inherent capability. We say that the parameters of an energy model are learnable iff there exists at least one set of such parameters that renders every known RNA structure to date the minimum free energy structure. We derive a necessary condition for the learnability and give a dynamic programming algorithm to assess it. Our algorithm computes the convex hull of the feature vectors of all feasible structures in the ensemble of a given input sequence. Interestingly, that convex hull coincides with the Newton polytope of the partition function as a polynomial in energy parameters. We demonstrated the application of our theory to a simple energy model consisting of a weighted count of A-U and C-G base pairs. Our results show that this simple energy model satisfies the necessary condition for less than one third of the input unpseudoknotted sequence-structure pairs chosen from the RNA STRAND v2.0 database. For another one third, the necessary condition is barely violated, which suggests that augmenting this simple energy model with more features such as the Turner loops may solve the problem. The necessary condition is severely violated for 8%, which provides a small set of hard cases that require further investigation.
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