论文标题
稀疏的马蹄估计通过预期最大化
Sparse Horseshoe Estimation via Expectation-Maximisation
论文作者
论文摘要
众所周知，马蹄形的先验具有许多理想的特性，用于贝叶斯对稀疏参数矢量的估计，但其密度函数缺乏分析形式。因此，为后验模式找到封闭形式的解决方案是一项挑战。常规的马蹄估计器使用后均值来估计参数，但这些估计并不稀少。我们提出了一个新型的期望最大化（EM）程序，用于计算标准线性模型的参数的地图估计值。我们方法的一个特殊优势是，m-step仅取决于先前的形式，并且独立于可能性。我们介绍了此EM过程的几个简单修改，这些修改允许直接扩展到广义线性模型。在对模拟和真实数据进行的实验中，我们的方法在统计绩效和计算成本方面执行了可比或优越的稀疏估计方法。
The horseshoe prior is known to possess many desirable properties for Bayesian estimation of sparse parameter vectors, yet its density function lacks an analytic form. As such, it is challenging to find a closed-form solution for the posterior mode. Conventional horseshoe estimators use the posterior mean to estimate the parameters, but these estimates are not sparse. We propose a novel expectation-maximisation (EM) procedure for computing the MAP estimates of the parameters in the case of the standard linear model. A particular strength of our approach is that the M-step depends only on the form of the prior and it is independent of the form of the likelihood. We introduce several simple modifications of this EM procedure that allow for straightforward extension to generalised linear models. In experiments performed on simulated and real data, our approach performs comparable, or superior to, state-of-the-art sparse estimation methods in terms of statistical performance and computational cost.
