Multi-task attributed graphical lasso and its application in fund classification.

Sparse inverse covariance estimation, i.e., Graphical Lasso, reveals the underlying structure of graph for a set of variables on the basis of their observations. The estimated graphs can then facilitate a series of downstream tasks with graph mining techniques. Multi-task Graphical Lasso is designed for collectively estimating graphs sharing an identical set of variables, but it fails to contend with the situation when the tasks include different variables. In order to address this limitation, we propose Multi-task Attributed Graphical Lasso (MAGL) to learn graphs with observations and attributes jointly. Specifically, we introduce two concrete implementations, i.e., MAGL-LogDet and MAGL-HSIC, where the LogDet divergence and the Hilbert-Schmidt independence criterion are utilized respectively to explore latent relations between attributes of the variables and linkage structures among the variables. Experimental results show the effectiveness of MAGL-LogDet and MAGL-HSIC. We then apply MAGL to fund data and estimate stock graphs for each fund. We classify funds by using graph neural networks on the estimated graphs, and prove that we can benefit from MAGL in downstream tasks. [ABSTRACT FROM AUTHOR]