Concept Drift

Learning-based Android malware detectors degrade over time due to natural distribution drift caused by malware variants and new families. This paper systematically investigates the challenges classifiers trained with empirical risk minimization (ERM) face against such distribution shifts and attributes their shortcomings to their inability to learn stable discriminative features. Invariant learning theory offers a promising solution by encouraging models to generate stable representations across environments that expose the instability of the training set. However, the lack of prior environment labels, the diversity of drift factors, and low-quality representations caused by diverse families make this task challenging. To address these issues, we propose TIF, the first temporal invariant training framework for malware detection, which aims to enhance the ability of detectors to learn stable representations across time. TIF organizes environments based on application observation dates to reveal temporal drift, integrating specialized multi-proxy contrastive learning and invariant gradient alignment to generate and align environments with high-quality, stable representations. TIF can be seamlessly integrated into any learning-based detector. Experiments on a decade-long dataset show that TIF excels, particularly in early deployment stages, addressing real-world needs and outperforming state-of-the-art methods.

The principal objective of this work is twofold within nonparametric regression settings: (1) to establish the minimax optimal convergence rates for fixed-bandwidth Gaussian kernel spectral algorithms when the true regression function resides in a Sobolev space, and (2) to apply Gaussian spectral algorithms for achieving robust and adaptive transfer learning under concept shift. While minimax optimality of misspecified spectral algorithms has been established, existing guarantees are typically restricted to the non-saturation regime. We demonstrate that the infinite smoothness of fixed-bandwidth Gaussian kernels provides universal robustness to model misspecification by showing that this kernel choice enables any spectral algorithm to attain minimax optimal rates, provided the regularization parameter decays exponentially. This result effectively decouples optimality from the algorithm's inherent qualification. Building on this, we then advocate Gaussian spectral algorithms as powerful components in a learning framework for robust and adaptive transfer. Specifically, we derive the adaptive convergence rate of the excess risk for this framework and show that the rates are optimal up to logarithmic factors. Our results also reveal the impact of the magnitude of the concept shift and the sample size on the generalization error.