We revisit Cox's proportional hazard models and LASSO in the aim of improving feature selection in survival analysis. Unlike traditional methods relying on cross-validation or BIC, the penalty parameter $\lambda$ is directly tuned for feature selection and is asymptotically pivotal thanks to taking the square root of Cox's partial likelihood. Substantially improving over both cross-validation LASSO and BIC subset selection, our approach has a phase transition on the probability of retrieving all and only the good features, like in compressed sensing. The method can be employed by linear models but also by artificial neural networks.

翻译：本文重新审视Cox比例风险模型与LASSO方法，旨在改进生存分析中的特征选择。与传统依赖交叉验证或BIC的方法不同，我们通过对Cox偏似然函数取平方根，使惩罚参数$\lambda$可直接用于特征选择，并具有渐近枢轴性。相较于交叉验证LASSO和BIC子集选择方法，本方法在准确识别全部有效特征的概率方面呈现相变现象，其特性类似于压缩感知理论中的表现。该方法不仅适用于线性模型，亦可扩展至人工神经网络架构。