Alzheimer’s disease (AD) is a slowly progressing neurodegenerative disorder and poses significant challenges for early diagnosis and longitudinal prognosis in the medical sector. Accurate prediction of cognitive decline is crucial for timely clinical intervention, disease monitoring, and treatment planning. Multi-task learning (MTL) has been extensively applied in AD prediction tasks, as it effectively captures shared patterns across multiple objectives and improves generalization. However, most existing MTL-based approaches focus on cross-sectional settings and lack the ability to explicitly model disease progression over time. To address this limitation, we propose a longitudinal multi-task learning framework that jointly models disease progression and adaptive temporal relationships using multi-timepoint neuroimaging data. The proposed method incorporates two task-specific projection matrices within a mixed-effects modeling framework to disentangle baseline-invariant representations from change-sensitive features, thereby capturing distinct patterns attributable to AD pathology and normal aging. Temporal relationships among tasks are learned directly from data via a task relationship matrix, while temporal asymmetry is enforced through directional regularization. Structured regularization is further introduced to enhance the sparsity and robustness of the learned model. The proposed framework is evaluated on real-world datasets from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) using standard regression metrics, including root mean squared error (rMSE). Compared with the best-performing baselines, our model achieves an average rMSE reduction of approximately 6%–10% across three widely used cognitive measures at multiple time points, with improvements validated by statistical significance testing, indicating more accurate and reliable prediction of cognitive decline. Beyond predictive accuracy, the model also provides enhanced interpretability through brain-region-level visualization, which facilitates a clearer understanding of disease-related progression patterns and age-related effects, and supports clinical analysis and decision-making.
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