高效正则化保序回归及其在基因-基因交互搜索中的应用
Efficient regularized isotonic regression with application to gene--gene interaction search
AI总结：
提出基于递归划分的正则化保序回归算法IRP，通过控制模型复杂度解决高维过拟合问题，并应用于基因-基因交互搜索。
摘要：
保序回归是一种用于拟合数据单调模型的非参数方法，在理论和实践上都得到了广泛研究。然而，该方法在高维中会遇到计算和统计过拟合问题。为了解决这两个问题，我们提出了一种算法，称为保序递归划分（IRP），该算法基于递归划分协变量空间，通过求解逐渐变小的“最佳切割”子问题来实现保序回归。这创建了一个正则化的保序模型序列，模型复杂度逐渐增加，并收敛到全局保序回归解。由于提供了复杂度控制，序列中的模型通常比未正则化的保序回归模型更准确。我们通过沿路径估计自由度来量化这种复杂度控制。通过一系列模拟和真实数据实验，证明了正则化模型在预测中的成功以及IRP良好的计算性能。我们讨论了IRP在搜索基因-基因交互和上位性中的应用，并在三种常见疾病的全基因组关联研究数据上进行了演示。
英文摘要：
Isotonic regression is a nonparametric approach for fitting monotonic models to data that has been widely studied from both theoretical and practical perspectives. However, this approach encounters computational and statistical overfitting issues in higher dimensions. To address both concerns, we present an algorithm, which we term Isotonic Recursive Partitioning (IRP), for isotonic regression based on recursively partitioning the covariate space through solution of progressively smaller "best cut" subproblems. This creates a regularized sequence of isotonic models of increasing model complexity that converges to the global isotonic regression solution. The models along the sequence are often more accurate than the unregularized isotonic regression model because of the complexity control they offer. We quantify this complexity control through estimation of degrees of freedom along the path. Success of the regularized models in prediction and IRPs favorable computational properties are demonstrated through a series of simulated and real data experiments. We discuss application of IRP to the problem of searching for gene--gene interactions and epistasis, and demonstrate it on data from genome-wide association studies of three common diseases.
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