ICML 2025

Censor Dependent Variational Inference
Chuanhui Liu 1 Xiao Wang 1
Abstract
This paper provides a comprehensive analysis
of variational inference in latent variable models
for survival analysis, emphasizing the distinctive
challenges associated with applying variational
methods to survival data. We identify a critical
weakness in the existing methodology, demon-
strating how a poorly designed variational distri-
bution may hinder the objective of survival anal-
ysis tasks—modeling time-to-event distributions.
We prove that the optimal variational distribu-
tion, which perfectly bounds the log-likelihood,
may depend on the censoring mechanism. To
address this issue, we propose censor-dependent
variational inference (CDVI), tailored for latent
variable models in survival analysis. More prac-
tically, we introduce CD-CVAE, a V-structure
Variational Autoencoder (VAE) designed for the
scalable implementation of CDVI. Further discus-
sion extends some existing theories and training
techniques to survival analysis. Extensive experi-
ments validate our analysis and demonstrate sig-
nificant improvements in the estimation of indi-
vidual survival distributions. Codes can be found
at https://github.com/ChuanhuiLiu/CDVI.
1. Introduction
Survival analysis, a fundamental topic in statistics, finds
wide-ranging applications across healthcare, insurance, qual-
ity management, and finance (Harrell et al., 2001; Nelson,
2005; Frees, 2009). It focuses on modeling the relation-
ship between time-to-event outcomes and individual demo-
graphic covariates, where the event of interest could be
death, disease progression, or similar occurrences. A key
challenge in survival analysis arises from censored obser-
vations, which provide only partial information about the
survival time, necessitating specialized methods to handle
1Department of Statistics, Purdue University, USA. Correspon-
dence to: Xiao Wang <wangxiao@purdue.edu>.
Proceedings of the 42 nd International Conference on Machine
Lea...