Transfer learning for high-dimensional transelliptical graphical models

This paper considers the problem of estimating high-dimensional transelliptical graphical models in the context of transfer learning where, in addition to observed target data, auxiliary samples (typically, the large majority) from different yet potentially related distributions are available. We propose a three-stage method called Trans-TE-CLIME, which simultaneously achieves modeling flexibility and estimation robustness by leveraging Kendall's tau statistics and incorporating information from auxiliary samples through a well-defined similarity measure. Theoretically, we derive convergence rates under both the column-wise (Formula presented.) norm and the Frobenius norm, demonstrating that sufficiently related auxiliary samples can accelerate convergence rates and thereby improve estimation accuracy. From a computational perspective, we propose two different algorithms for the oracle case with known transferable sources and more realistic case with non-informative sources, respectively. The optimization procedure in each stage can be decomposed into some linear programming problems, rendering our method scalable to large datasets. Empirically, simulation studies confirm the outstanding numerical performance of the Trans-TE-CLIME method. We also apply our proposed method to a stock dataset, yielding some insightful conclusions. The complete code supporting this study can be downloaded from https://github.com/zyhnku/Trans-TE-CLIME.