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This research introduces a novel multitask regression framework that adapts coefficient sharing strategies based on specific predictors, moving beyond uniform pooling to handle heterogeneous task structures. By penalizing pairwise differences and incorporating group penalties for predictor selection, the method achieves tight theoretical bounds while effectively modeling scenarios where most tasks share coefficients but exceptions exist. Simulations and household energy data demonstrate its ability to seamlessly transition between broad sharing and task-specific coefficient estimation.
Multitask Regression with Pairwise Fusion
arXiv:2609.27280v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2609.27280 [stat.ML]
(or arXiv:2609.27280v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2609.27280 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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