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Multi-task Highly Adaptive Lasso

27 January 2023
Ivana Malenica
Rachael V. Phillips
D. Lazzareschi
Jeremy Coyle
Romain Pirracchio
Mark van der Laan
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Abstract

We propose a novel, fully nonparametric approach for the multi-task learning, the Multi-task Highly Adaptive Lasso (MT-HAL). MT-HAL simultaneously learns features, samples and task associations important for the common model, while imposing a shared sparse structure among similar tasks. Given multiple tasks, our approach automatically finds a sparse sharing structure. The proposed MTL algorithm attains a powerful dimension-free convergence rate of op(n−1/4)o_p(n^{-1/4})op​(n−1/4) or better. We show that MT-HAL outperforms sparsity-based MTL competitors across a wide range of simulation studies, including settings with nonlinear and linear relationships, varying levels of sparsity and task correlations, and different numbers of covariates and sample size.

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