这篇论文提出了一个解决多任务学习中不同任务类型结果不可比较问题的框架，使用了共享稀疏性和深度网络，理论扎实，还有基因数据实验，搞统计学习和生物信息的朋友可以看看。
该论文提出一种多任务变换框架，通过未知单调变换处理不同类型的任务响应。在预测变量维度随样本量增长的高维生物学场景下，仅部分公共预测子有效，论文引入跨任务共享稀疏性。方法通过共享第一层的深度神经网络优化基于秩的平滑准则并施加group-Lasso惩罚。非渐近超额风险界和变量选择一致性得到理论证明。在基因表达数据（连续、二值、混合结果）上比现有方法预测更优，并识别出有生物学意义的共享预测子。
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.