# Multitask Regression with Pairwise Fusion

arXiv: https://arxiv.org/abs/2609.27280 · HTML: https://mlsanity.com/paper/2609.27280/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 5 of 5)

- [Network Lasso: Clustering and Optimization in Large Graphs](https://mlsanity.com/paper/1507.00280/) (2015)
- [Total Variation Classes Beyond 1d: Minimax Rates, and the Limitations of Linear Smoothers](https://mlsanity.com/paper/1605.08400/) (2016)
- [A concave pairwise fusion approach to subgroup analysis](https://mlsanity.com/paper/1508.07045/) (2015)
- [Multi-Task Learning Regression via Convex Clustering](https://mlsanity.com/paper/2304.13342/) (2023)
- [High-dimensional regression over disease subgroups](https://mlsanity.com/paper/1611.00953/) (2016)

## Abstract (arXiv)

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.