This paper considers clustered multi-task compressive sensing, a hierarchical
model that solves multiple compressive sensing tasks by finding clusters of
tasks that leverage shared information to mutually improve signal
reconstruction. The existing inference algorithm for this model is
computationally expensive and does not scale well in high dimensions. The main
bottleneck involves repeated matrix inversion and log-determinant computation
for multiple large covariance matrices. We propose a new algorithm that
substantially accelerates model inference by avoiding the need to explicitly
compute these covariance matrices. Our approach combines Monte Carlo sampling
with iterative linear solvers. Our experiments reveal that compared to the
existing baseline, our algorithm can be up to thousands of times faster and an
order of magnitude more memory-efficient.

本文提出了一种新的算法，通过避免显式计算协方差矩阵结合蒙特卡洛抽样和迭代线性求解器，从而大大加速模型推断。与现有基准相比，实验表明我们的算法在速度上可快数千倍，内存利用率提升一个数量级。