论文标题
图形信号使用$ t $ -shrinkage先验
Graph signal denoising using $t$-shrinkage priors
论文作者
论文摘要
我们通过在无方向的图上估算分段常数信号来研究图形信号降解问题。我们提出了一种新的贝叶斯方法，该方法首先通过深度优先搜索算法将一般图转换为链图，然后在诱导链图上连续信号之间的差异施加了重尾$ t $ shrinkage。我们表明，可以通过充分探索模型中的共轭结构来方便地进行后验计算。我们还得出了所提出的估计器的后验收缩率，并表明该速率是最佳的，除了自动适应图形的未知边缘稀疏度外，还具有对数因子。我们通过广泛的仿真研究和对股票市场数据的应用来证明该方法的出色经验性能。
We study the graph signal denoising problem by estimating a piecewise constant signal over an undirected graph. We propose a new Bayesian approach that first converts a general graph to a chain graph via the depth-first search algorithm, and then imposes a heavy-tailed $t$-shrinkage prior on the differences between consecutive signals over the induced chain graph. We show that the posterior computation can be conveniently conducted by fully exploring the conjugacy structure in the model. We also derive the posterior contraction rate for the proposed estimator, and show that this rate is optimal up to a logarithmic factor, besides automatically adapting to the unknown edge sparsity level of the graph. We demonstrate the excellent empirical performance of the proposed method via extensive simulation studies and applications to stock market data.
