Xing Zhengrong, Carbonetto Peter, Stephens Matthew
Department of Statistics, University of Chicago, Chicago, IL 60637, USA.
Research Computing Center and Department of Human Genetics, University of Chicago, Chicago, IL 60637, USA.
J Mach Learn Res. 2021 Jan-Dec;22.
Signal denoising-also known as non-parametric regression-is often performed through shrinkage estimation in a transformed (e.g., wavelet) domain; shrinkage in the transformed domain corresponds to smoothing in the original domain. A key question in such applications is how much to shrink, or, equivalently, how much to smooth. Empirical Bayes shrinkage methods provide an attractive solution to this problem; they use the data to estimate a distribution of underlying "effects," hence automatically select an appropriate amount of shrinkage. However, most existing implementations of empirical Bayes shrinkage are less flexible than they could be-both in their assumptions on the underlying distribution of effects, and in their ability to handle heteroskedasticity-which limits their signal denoising applications. Here we address this by adopting a particularly flexible, stable and computationally convenient empirical Bayes shrinkage method and applying it to several signal denoising problems. These applications include smoothing of Poisson data and heteroskedastic Gaussian data. We show through empirical comparisons that the results are competitive with other methods, including both simple thresholding rules and purpose-built empirical Bayes procedures. Our methods are implemented in the R package smashr, "SMoothing by Adaptive SHrinkage in R," available at https://www.github.com/stephenslab/smashr.
信号去噪（也称为非参数回归）通常通过在变换域（例如小波域）中进行收缩估计来实现；变换域中的收缩对应于原始域中的平滑。此类应用中的一个关键问题是收缩多少，或者等效地说，平滑多少。经验贝叶斯收缩方法为这个问题提供了一个有吸引力的解决方案；它们使用数据来估计潜在“效应”的分布，从而自动选择适当的收缩量。然而，经验贝叶斯收缩的大多数现有实现都不如它们本可以的那样灵活——无论是在对效应潜在分布的假设方面，还是在处理异方差的能力方面——这限制了它们在信号去噪中的应用。在这里，我们通过采用一种特别灵活、稳定且计算方便的经验贝叶斯收缩方法并将其应用于几个信号去噪问题来解决这个问题。这些应用包括泊松数据和异方差高斯数据的平滑。我们通过实证比较表明，结果与其他方法具有竞争力，包括简单的阈值规则和专门构建的经验贝叶斯程序。我们的方法在R包smashr（“R中的自适应收缩平滑”）中实现，可在https://www.github.com/stephenslab/smashr获取。
