On the Statistical Efficiency of $\ell_{1,p}$ Multi-Task Learning of Gaussian Graphical Models
This work addresses statistical efficiency in multi-task learning for graphical models, which is incremental as it builds on existing methods with new theoretical bounds.
The paper tackles the problem of multi-task structure learning for Gaussian graphical models by analyzing the sample complexity for correct support union and edge sign recovery, comparing multi-task to single-task learning, and providing experimental validation on synthetic and real-world datasets.
In this paper, we present $\ell_{1,p}$ multi-task structure learning for Gaussian graphical models. We analyze the sufficient number of samples for the correct recovery of the support union and edge signs. We also analyze the necessary number of samples for any conceivable method by providing information-theoretic lower bounds. We compare the statistical efficiency of multi-task learning versus that of single-task learning. For experiments, we use a block coordinate descent method that is provably convergent and generates a sequence of positive definite solutions. We provide experimental validation on synthetic data as well as on two publicly available real-world data sets, including functional magnetic resonance imaging and gene expression data.