Multi-task Highly Adaptive Lasso
Ivana Malenica, Rachael V. Phillips, Daniel Lazzareschi, Jeremy R., Coyle, Romain Pirracchio, Mark J. van der Laan

TL;DR
The paper introduces MT-HAL, a nonparametric multi-task learning method that automatically discovers shared sparse structures among tasks, achieving fast convergence and outperforming existing methods in diverse simulations.
Contribution
It presents a novel, fully nonparametric multi-task learning approach that learns feature, sample, and task associations with a shared sparse structure, along with a fast convergence rate.
Findings
Outperforms existing sparsity-based MTL methods in simulations
Effective in both linear and nonlinear settings
Achieves a convergence rate of o_p(n^{-1/4}) or better
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 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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Taxonomy
TopicsGaussian Processes and Bayesian Inference · Statistical Methods and Inference · Energy Load and Power Forecasting
