We present neural frailty machine (NFM), a powerful and flexible neural modeling framework for survival regressions. The NFM framework utilizes the classical idea of multiplicative frailty in survival analysis to capture unobserved heterogeneity among individuals, at the same time being able to leverage the strong approximation power of neural architectures for handling nonlinear covariate dependence. Two concrete models are derived under the framework that extends neural proportional hazard models and nonparametric hazard regression models. Both models allow efficient training under the likelihood objective. Theoretically, for both proposed models, we establish statistical guarantees of neural function approximation with respect to nonparametric components via characterizing their rate of convergence. Empirically, we provide synthetic experiments that verify our theoretical statements. We also conduct experimental evaluations over $6$ benchmark datasets of different scales, showing that the proposed NFM models outperform state-of-the-art survival models in terms of predictive performance. Our code is publicly availabel at https://github.com/Rorschach1989/nfm

翻译：我们提出了神经衰弱机器（NFM），这是一种强大且灵活的神经建模框架，用于生存回归。该框架利用生存分析中乘性衰弱的经典思想来捕捉个体间未观察到的异质性，同时能够利用神经架构的强大近似能力处理非线性协变量依赖。在该框架下，我们推导出两个具体模型，分别扩展了神经比例风险模型和非参数风险回归模型。这两个模型均支持在似然目标下进行高效训练。理论方面，对于所提出的两个模型，我们通过刻画其收敛速度，为非参数组件的神经函数逼近建立了统计保证。实验方面，我们通过合成实验验证了理论结果，并在6个不同规模的基准数据集上进行了评估，结果表明所提出的NFM模型在预测性能上优于最先进的生存模型。我们的代码公开于 https://github.com/Rorschach1989/nfm。