多任务回归与成对融合
Multitask Regression with Pairwise Fusion
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中文总结 AI 辅助
本研究提出一种成对融合惩罚的多任务回归方法，通过惩罚跨任务系数差异并附加组惩罚，实现系数共享结构估计，并在理论上证明其上下界一致，实验验证了其有效性。
中文摘要 AI 辅助
我们研究当系数共享可能因预测变量而异时的多任务回归问题。对于给定的预测变量，许多任务可能具有相同的系数，而少数任务则不同，并且这些异常任务对于另一个预测变量而言可能并不相同。我们通过两个量来描述这种结构：活跃预测变量的数量，以及与其预测变量最常见值不同的任务系数的总数。我们通过惩罚跨任务的所有成对系数差异来估计系数矩阵，并在需要预测变量选择时附加一个组惩罚。由此得到的上界和下界对这两个量具有相同的依赖性。我们还考虑了更强的设定，即一大组任务共享一个完整的系数向量。在明确的样本量条件下，相同的成对估计器会精确地合并这些任务，同时允许其余任务有所不同。模拟实验和家庭能源数据展示了广泛共享与任务特定系数之间的过渡。
英文摘要
We study multitask regression when coefficient sharing can differ by predictor. For a given predictor, many tasks may have the same coefficient while a few differ, and the exceptional tasks need not be the same for another predictor. We describe this structure by two quantities: the number of active predictors and the total number of task coefficients that differ from the most common value for their predictor. We estimate the coefficient matrix by penalizing all pairwise coefficient differences across tasks, with an additional group penalty when predictor selection is needed. The resulting upper and lower bounds have the same dependence on these two quantities. We also consider the stronger setting in which a large set of tasks shares one entire coefficient vector. Under explicit sample-size conditions, the same pairwise estimator pools those tasks exactly, while allowing the remaining tasks to differ. Simulations and household energy data illustrate the transition between broad sharing and task-specific coefficients.
发表机构
- University of California, Davis（加州大学戴维斯分校）
机构由 AI 辅助整理，请以论文原文为准。
