Survival analysis concerns the study of timeline data where the event of interest may remain unobserved (i.e., censored). Studies commonly record more than one type of event, but conventional survival techniques focus on a single event type. We set out to integrate both multiple independently censored time-to-event variables as well as missing observations. An energy-based approach is taken with a bi-partite structure between latent and visible states, known as harmoniums (or restricted Boltzmann machines). The present harmonium is shown, both theoretically and experimentally, to capture non-linearly separable patterns between distinct time recordings. We illustrate on real world data that, for a single time-to-event variable, our model is on par with established methods. In addition, we demonstrate that discriminative predictions improve by leveraging an extra time-to-event variable. In conclusion, multiple time-to-event variables can be successfully captured within the harmonium paradigm.

翻译：生存分析关注事件时间数据的研究，其中目标事件可能未被观测到（即存在删失）。研究通常记录多种事件类型，但传统生存分析方法聚焦于单一事件类型。我们旨在整合多个独立删失的时间-事件变量以及缺失观测数据。本文采用基于能量的方法，通过潜在状态与可见状态之间的二分结构（即和谐机或受限玻尔兹曼机）实现。理论上与实验上均证明，当前和谐机能够捕捉不同时间记录之间的非线性可分模式。我们通过真实数据表明，对于单一时间-事件变量，本模型与成熟方法性能相当。此外，我们证明利用额外的时间-事件变量可提升判别性预测效果。结论表明，和谐机范式能成功捕捉多个时间-事件变量。