An Efficient Algorithm for Clustered Multi-Task Compressive Sensing
Alexander Lin Demba Ba
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.