论文标题
没有协方差矩阵的高维稀疏贝叶斯学习
High-Dimensional Sparse Bayesian Learning without Covariance Matrices
论文作者
论文摘要
稀疏的贝叶斯学习（SBL）是解决稀疏编码问题的有力框架。但是，由于需要存储和计算一个大协方差矩阵，因此最流行的SBL推理算法对于高维设置而变得太昂贵了。我们引入了一种新的推理方案，该方案通过并行求解多个线性系统来避免显式构建协方差矩阵，以获得SBL的后矩。我们的方法将鲜为人知的对角线估计与结合梯度算法产生。在几个模拟中，我们的方法比计算时间和内存中现有方法更好，尤其是对于能够快速矩阵矢量乘法的结构化词典。
Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem. However, the most popular inference algorithms for SBL become too expensive for high-dimensional settings, due to the need to store and compute a large covariance matrix. We introduce a new inference scheme that avoids explicit construction of the covariance matrix by solving multiple linear systems in parallel to obtain the posterior moments for SBL. Our approach couples a little-known diagonal estimation result from numerical linear algebra with the conjugate gradient algorithm. On several simulations, our method scales better than existing approaches in computation time and memory, especially for structured dictionaries capable of fast matrix-vector multiplication.
