General Risk Minimization under Random Censorship with Empirical Likelihood Weighting

刘玉坤，华东师范大学统计学院教授、博士生导师，国家级高层次人才计划入选者。本科与博士均毕业于南开大学统计系，此后一直在华东师范大学任教。研究方向涵盖分布偏移数据、因果推断、共形推断、半参数统计与机器学习等。研究成果发表于JRSSB、 AOS、 JASA、 Biometrika、 Biometrics、 JOE 等国际期刊，以及 NeurIPS、ICLR 等计算机领域顶级会议；现担任教育部“生态安全的智慧决策”学科突破先导项目PI，主持科技部国家重点研发计划课题与国家自然科学基金项目。

Empirical Risk Minimization (ERM) serves as a foundational framework in statistical learning and machine learning, yet conventional ERM methods struggle with censored data, which are common in various fields. The inherent censoring mechanism generates incomplete observations that disrupt direct loss function evaluation. While inverse probability of censoring weighting (IPCW) methods--based on the conditional survival function $S_C(t|\bx)$--partially mitigate this issue, they exhibit severe instability as $S_C(t|\bx)$ approaches zero. We propose an empirical likelihood weighting-based ERM (ELW-ERM), which overcomes the instability issues associated with IPCW and accommodates general loss functions, including squared loss, logistic loss and quantile loss. We establish non-asymptotic or asymptotic error bounds on the excess risk of our ELW-ERM predictor under general conditions and three specific model assumptions. Our ELW-ERM is shown to achieve the same learning rates as classical ERMs in absence of censoring under the Cox model, and as the IPCW-based ERM under a fully nonparametric model. Under a general Cox model, with the help of deep neural networks, it is able to mitigate the curse-of-dimensionality issue when $S_{C}(t|\bx)$ has a low-dimensional structure. Numerical experiments and an empirical analysis demonstrate the effectiveness and superiority of our proposed ELW-ERM method.