Transfer Learning in High-dimensional Ising Models

Existing methods for transfer learning struggle to deal with situations where the source datasets are limited and not guaranteed to be well-aligned with the target dataset. A typical strategy is to use the empirical loss minimizer on the source data as a prior mean for the target parameters. Our key conceptual contribution is to use a risk minimizer conditional on source parameters instead. This allows us to construct a single joint prior distribution for all parameters from the source datasets as well as the target dataset. As a consequence, we benefit from full Bayesian uncertainty quantification and can perform model averaging via Gibbs sampling over indicator variables governing the inclusion of each source dataset. We show how a particular instantiation of our prior leads to a Bayesian Lasso in a transformed coordinate system and discuss computational techniques to scale our approach to moderately sized datasets. We discuss connections between the Maximum a Posteriori estimate associated with our approach and the recently proposed Trans-Lasso method and demonstrate that the MAP estimator MSE-dominates the Trans-Lasso in the normal means setting when there is no regularization on the source datasets. Finally, we perform numerical experiments finding that full Bayesian inference provides superior predictive performance relative to Trans-Lasso on a genetics application, especially when the source data are limited.

Multi-task learning is effective for related applications, but its performance can deteriorate when the target sample size is small. Transfer learning can borrow strength from related studies; yet, many existing methods rely on restrictive bounded-difference assumptions between the source and target models. We propose SMART, a spectral transfer method for multi-task linear regression that instead assumes spectral similarity: the target left and right singular subspaces lie within the corresponding source subspaces and are sparsely aligned with the source singular bases. Such an assumption is natural when studies share latent structures and enables transfer beyond the bounded-difference settings. SMART estimates the target coefficient matrix through structured regularization that incorporates spectral information from a source study. Importantly, it requires only a fitted source model rather than the raw source data, making it useful when data sharing is limited. Although the optimization problem is nonconvex, we develop a practical ADMM-based algorithm. We establish general, non-asymptotic error bounds and a minimax lower bound in the noiseless-source regime. Under additional regularity conditions, these results yield near-minimax Frobenius error rates up to logarithmic factors. Simulations confirm improved estimation accuracy and robustness to negative transfer, and analysis of multi-modal single-cell data demonstrates better predictive performance. The Python implementation of SMART, along with the code to reproduce all experiments in this paper, is publicly available at https://github.com/boxinz17/smart.

Transfer learning is a natural strategy when a target population has limited data but multiple related auxiliary sources are available. A central difficulty is source heterogeneity: auxiliary sources may not be equally useful, and their usefulness may vary in a structured, cluster-like fashion. Existing transfer-learning methods often reduce source selection to a binary informative/non-informative decision, overlooking subgroups of sources with differential transferability. Motivated by a suicide-risk study using data from the Connecticut Hospital Information Management Exchange (CHIME), comprising 636,758 patients across 27 hospitals, we propose Trans-GLMC, a cluster-structured transfer-learning procedure for generalized linear models. The CHIME setting illustrates the core challenge: hospital-specific risk models are unstable because suicide attempts are rare at any single facility, whereas indiscriminate pooling across hospitals can obscure facility-level differences in patient mix and risk profiles. Trans-GLMC first constructs a coefficient-based distance among the target and candidate sources to recover latent source clusters. It then combines global fusion, within-cluster refinement, and target debiasing to produce an estimator that adapts to the detected structure. We establish a non-asymptotic error bound that improves over its unclustered counterpart whenever a meaningful target cluster exists and matches the unclustered rate up to constants otherwise. In simulations and in the CHIME study, Trans-GLMC improves facility-specific prediction, identifies interpretable communities of hospitals with mutual transferability, and recovers clinically coherent suicide-risk factors.