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.

Many scientific and social datasets record yes-or-no information, such as whether a gene is mutated, whether a customer bought an item, or whether a user liked a movie. A common goal is to understand how these variables are related to one another, but this can be difficult when the dataset of main interest is small. Related datasets may help, but using all of them without checking can make the result worse if some of them come from different populations or settings. We propose Trans-Ising, a method that helps learn networks from binary data by using related datasets more safely. It first checks which additional datasets appear useful for the main dataset, and then combines the selected information with a correction step based only on the main dataset. This design aims to benefit from extra data while reducing the risk of negative transfer. Our theory shows when this approach can improve estimation and recover the underlying network structure under suitable conditions. In experiments with simulated data and real datasets, Trans-Ising gives more accurate results than using only the main dataset or simply pooling all available datasets.