Multi-task Highly Adaptive Lasso

2023/01/27 by Ivana Malenica, Malenica, Ivana, Rachael V. Phillips +9
Computer Science · Engineering · Mathematics · #Energy Load and Power Forecasting #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2301.12029

openalex publication_date 2023/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 o_p(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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