Domain adaptation enables generalizable and efficient data-driven research. However, existing work has largely focused on domain adaptation for some intrinsically homogeneous target cohort, overlooking inherent heterogeneity within the target, which can exacerbate biases and unfairness in the presence of subgroups with imbalanced sample sizes. We develop a novel domain adaptation framework that addresses a more complicated target dataset that consists of heterogeneous and data-sparse subgroups and lacks gold-standard label observations. Our method simultaneously handles high-dimensionality, covariate shift, and outcome model heterogeneity by combining a model-assisted debiasing step used for covariate shift correction with an adaptive knowledge-guided sparsification procedure used to mitigate the issue of sample disparity. We also introduce a new model selection strategy to avoid negative knowledge transfer in the absence of labels in the target data. Our method is theoretically justified for being robust to nuisance model misspecification and adaptive to heterogeneity between the subgroups. Numerical experiments and two real-world applications, including genetic risk modeling of type 2 diabetes and prediction of mutation-induced protein stability changes, demonstrate the practical advantages of our method.

Unsupervised feature selection has drawn wide attention in the era of big data, since it serves as a fundamental technique for dimensionality reduction. However, many existing unsupervised feature selection models and solution methods are primarily designed for practical applications, and often lack rigorous theoretical support, such as convergence guarantees. In this paper, we first establish a novel unsupervised feature selection model based on regularized minimization with nonnegative orthogonality constraints, which has advantages of embedding feature selection into the nonnegative spectral clustering and preventing overfitting. To solve the proposed model, we develop an effective inexact augmented Lagrangian multiplier method, in which the subproblems are addressed using a proximal alternating minimization approach. We rigorously prove the algorithm's sequence converges to a stationary point of the model. Extensive numerical experiments on popular datasets demonstrate the stability and robustness of our method. Moreover, comparative results show that our method outperforms some existing state-of-the-art methods in terms of clustering evaluation metrics. The code is available at https://github.com/liyan-amss/NOCRM_code.