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A Variational Bayes Framework for Sparse Adaptive Estimation

机译：稀疏自适应估计的变分贝叶斯框架

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摘要

Recently, a number of mostly $ell_1$ -norm regularized least-squares-type deterministic algorithms have been proposed to address the problem of sparse adaptive signal estimation and system identification. From a Bayesian perspective, this task is equivalent to maximum a posteriori probability estimation under a sparsity promoting heavy-tailed prior for the parameters of interest. Following a different approach, this paper develops a unifying framework of sparse variational Bayes algorithms that employ heavy-tailed priors in conjugate hierarchical form to facilitate posterior inference. The resulting fully automated variational schemes are first presented in a batch iterative form. Then, it is shown that by properly exploiting the structure of the batch estimation task, new sparse adaptive variational Bayes algorithms can be derived, which have the ability to impose and track sparsity during real-time processing in a time-varying environment. The most important feature of the proposed algorithms is that they completely eliminate the need for computationally costly parameter fine-tuning, a necessary ingredient of sparse adaptive deterministic algorithms. Extensive simulation results are provided to demonstrate the effectiveness of the new sparse adaptive variational Bayes algorithms against state-of-the-art deterministic techniques for adaptive channel estimation. The results show that the proposed algorithms are numerically robust and exhibit in general superior estimation performance compared to their deterministic counterparts.
机译：最近，已经提出了许多主要的 $ ell_1 $ -范数正则化最小二乘型确定性算法来解决该问题。稀疏自适应信号估计与系统辨识从贝叶斯角度看，此任务等效于在稀疏度下提升感兴趣参数的先验概率后的最大后验概率估计。按照不同的方法，本文开发了一个稀疏变分贝叶斯算法的统一框架，该算法使用共轭分层形式的重尾先验来促进后验推断。首先以批处理迭代的形式介绍生成的全自动变异方案。然后，表明通过适当地利用批估计任务的结构，可以导出新的稀疏自适应变分贝叶斯算法，该算法具有在时变环境中实时处理期间施加和跟踪稀疏性的能力。所提出算法的最重要特征是，它们完全消除了对计算上昂贵的参数微调的需求，这是稀疏自适应确定性算法的必要组成部分。提供了大量的仿真结果，以证明新的稀疏自适应变分贝叶斯算法相对于最新的自适应信道估计确定性技术的有效性。结果表明，与确定性算法相比，该算法具有较强的数值鲁棒性，并且在总体上具有优越的估计性能。

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