Transfer learning, as a machine learning approach enhancing model generalization across different domains, has extensive applications in various fields. However, the risk of privacy leakage remains a crucial consideration during the transfer learning process. Differential privacy, with its rigorous mathematical foundation, has been proven to offer consistent and robust privacy protection. This study delves into the logistic regression transfer learning problem supported by differential privacy. In cases where transferable sources are known, we propose a two-step transfer learning algorithm. For scenarios with unknown transferable sources, a non-algorithmic, cross-validation-based transferable source detection method is introduced, to mitigate adverse effects from non-informative sources. The effectiveness of the proposed algorithm is validated through simulations and experiments with real-world data.

With the widespread application of spatial data in fields like econometrics and geographic information science, the methods to enhance the robustness of spatial econometric model estimation and variable selection have become a central focus of research. In the context of the spatial error model (SEM), this paper introduces a variable selection method based on exponential square loss and the adaptive lasso penalty. Due to the non-convex and non-differentiable nature of this proposed method, convex programming is not applicable for its solution. We develop a block coordinate descent algorithm, decompose the exponential square component into the difference of two convex functions, and utilize the CCCP algorithm in combination with parabolic interpolation for optimizing problem-solving. Numerical simulations demonstrate that neglecting the spatial effects of error terms can lead to reduced accuracy in selecting zero coefficients in SEM. The proposed method demonstrates robustness even when noise is present in the observed values and when the spatial weights matrix is inaccurate. Finally, we apply the model to the Boston housing dataset.