Deep Multitask Learning for Mixed-Type Outcomes with Shared Sparsity
2026-07-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address a problem in multitask learning where different tasks have outcomes that can’t be easily compared because they use different scales or types of measurements. They propose a new method that assumes outcomes are related through unknown transformations and focus on identifying key predictors shared across tasks. Their approach uses a special rank-based criterion combined with a group-Lasso penalty implemented in a multitask neural network. They show mathematically that their method works well and, through simulations and gene-expression data, demonstrate it predicts accurately and finds meaningful common predictors.
multitask learningmonotone transformationsshared sparsitygroup-Lasso penaltyrank-based criteriondeep neural networkvariable selectionnonasymptotic risk boundsgene-expression analysis
Authors
Huichao Li, Tong Wang, Sanguo Zhang, Shuangge Ma
Abstract
Most existing multitask learning approaches are limited by their reliance on task-specific loss functions tailored to the scale and type of each outcome. When outcomes differ across tasks, these losses are generally not directly comparable, which makes it difficult to formulate a unified objective and may limit information sharing across tasks. We propose a multitask transformation framework in which task-specific responses may differ through unknown monotone transformations. Motivated by high-dimensional biological applications in which the predictor dimension may diverge with the sample size while only a common subset of predictors is informative, we consider shared sparsity across tasks. Under this framework, we estimate the target functions and identify important predictors by optimizing a smoothed rank-based criterion with a group-Lasso penalty, implemented through a multitask deep neural network with a shared first layer. We establish the nonasymptotic excess-risk bounds, and variable-selection consistency for the proposed estimator. Simulation studies show that the proposed method achieves competitive prediction and variable-selection performance compared with competing approaches. Analyses of gene-expression studies with continuous, binary, and mixed outcomes further illustrate that the proposed method improves prediction and identifies biologically meaningful shared predictors.