Transfer Learning in High-dimensional Ising Models

Abstract

We propose a transfer learning framework for estimating high-dimensional Ising models that characterize interactions between discrete binary variables from limited target samples and multiple auxiliary datasets of unknown relevance. Our algorithm, termed Trans-Ising, builds upon a two-stage procedure that first obtains an initial estimator via nodewise $\ell_1$-regularized logistic regression on the target data together with selected auxiliary samples, and then refines it using a target-only correction step with a folded-concave penalty to improve edge selection accuracy. To decide which auxiliary sources to transfer from and reduce the risk of negative transfer, we introduce a loss-based screening rule based on out-of-sample pseudolikelihood evaluation on held-out target data. We also establish asymptotic error bounds and selection consistency for the proposed estimator under standard high-dimensional conditions. Extensive simulations and real data applications show that Trans-Ising consistently outperforms competing methods.