The NFM framework utilizes the classical idea of multiplicative frailty in survival analysis as a principled way of extending the proportional hazard assumption, 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 achieve predictive performance comparable to or sometimes surpassing state-of-the-art survival models.

The NFM framework utilizes the classical idea of multiplicative frailty in survival analysis as a principled way of extending the proportional hazard assumption, 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.

Survival regression aims to predict the time when an event of interest will take place, typically a death or a failure. A fully parametric method [18] is proposed to estimate the survival function as a mixture of individual parametric distributions in the presence of censoring. In this paper, We present a novel method to predict the survival time by better clustering the survival data and combine primitive distributions. We propose two variants of variational auto-encoder (VAE), discrete and continuous, to generate the latent variables for clustering input covariates. The model is trained end to end by jointly optimizing the VAE loss and regression loss. Thorough experiments on dataset SUPPORT and FLCHAIN show that our method can effectively improve the clustering result and reach competitive scores with previous methods. We demonstrate the superior result of our model prediction in the long-term. Our code is available at https://github.com/

Real-world decision-making often requires reasoning about when an event will occur. The overarching goal of such reasoning is to help aid decision-making for optimal triage and subsequent intervention. Healthcare and Bio-informatics: More commonly known as'Survival Analysis' involves prognostication of an adverse physiological event like a stroke, the onset of cancer, re-hospitalization, and mortality. Time-to-event or survival analysis can be used to proactively mitigate adverse outcomes and extend the longevity of patients. Internet Marketing and e-commerce: Models employed for estimating customer churn and retention in large commercial organizations are essentially time-to-event regression models and help determine best practices to maximize customer retention.