Deep Multitask Model Unifies Mixed Outcomes via Shared Sparsity

Most multitask learning approaches falter when outcomes differ in type—loss functions become incomparable, limiting information sharing. To solve this, Li et al. introduce a transformation framework that learns unknown monotone mappings for each task, making losses directly comparable. They enforce shared sparsity across tasks via a group-Lasso penalty, assuming only a common subset of high-dimensional predictors is informative. The architecture uses a multitask deep neural network with a shared first layer, optimizing a smoothed rank-based criterion. The authors prove nonasymptotic excess-risk bounds and variable-selection consistency, providing theoretical rigor rare in deep learning.

Simulation studies show the method matches or outperforms existing approaches in prediction and variable selection, especially when outcomes mix continuous and binary types. Real-world validation on gene-expression datasets with continuous, binary, and mixed endpoints demonstrates improved prediction and discovery of biologically meaningful shared predictors. This framework offers a unified solution for heterogeneous biomedical data, where outcomes often vary (e.g., tumor size, survival status, mutation presence). By enabling joint learning across diverse outcomes, it paves the way for more robust multi-task models in high-dimensional settings.