Smoothing via Adaptive Shrinkage (smash): denoising Poisson and heteroskedastic Gaussian signals
We describe the idea of "Adaptive Shrinkage" (ASH), a general purpose Empirical Bayes (EB) method for shrinkage estimation, and demonstrate its application to several signal denoising problems. The ASH method takes as input a set of estimates and their corresponding standard errors, and outputs shrinkage estimates of the underlying quantities ("effects"). Compared with existing EB shrinkage methods, a key feature of ASH is its use of a flexible family of "unimodal" distributions to model the distribution of the effects. The approach is not only flexible and self-tuning, but also computationally convenient because it results in a convex optimization problem that can be solved quickly and reliably. Here we demonstrate the effectiveness and convenience of ASH by applying it to several signal denoising applications, including smoothing of Poisson and heteroskedastic Gaussian data. In both cases ASH consistently produces estimates that are as accurate -- and often more accurate -- than other shrinkage methods, including both simple thresholding rules and purpose-built EB procedures. We illustrate the potential for Poisson smoothing to provide an alternative to "peak finding" algorithms for sequencing assays such as Chromatin Immunoprecipitation (ChIP-Seq). The methods are implemented in an R package, "smashr" (SMoothing by Adaptive SHrinkage in R), available from http://www.github.com/stephenslab/smashr.
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