Deep Multitask Learning for Mixed-Type Outcomes with Shared Sparsity

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.