Transfer Learning in High-dimensional Ising Models

In high-dimensional Ising model estimation, target sample sizes are often limited, and effectively using auxiliary binary datasets of unknown relevance remains challenging.

To address this, we propose Trans-Ising, a transfer learning method that combines a loss-based source screening rule with a two-stage estimation procedure.

The method first identifies informative auxiliary sources using held-out target pseudolikelihood to prevent negative transfer.

It then computes an initial estimator via pooled nodewise $\ell_1$-regularized logistic regression, followed by a target-only correction step using a folded-concave penalty.

Theoretically, we establish fixed-node $\ell_2$ and $\ell_1$ error bounds, exact graph selection consistency, and the conditional consistency of the screening rule.

Through extensive simulations and real-data analyses, we demonstrate that Trans-Ising achieves lower estimation errors than both target-only estimation and naive data pooling.