Censor Dependent Variational Inference

TL;DR

This paper introduces censor-dependent variational inference (CDVI) for survival analysis, addressing challenges with censoring and proposing a scalable VAE-based method that improves survival distribution estimation.

Contribution

We identify the dependence of the optimal variational distribution on censoring and propose CDVI and CD-CVAE, novel methods tailored for survival analysis with censored data.

Findings

Significant improvement in survival distribution estimation.

Theoretical validation of censor-dependent variational bounds.

Scalable implementation via CD-CVAE.

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, demonstrating how a poorly designed variational distribution may hinder the objective of survival analysis tasks - modeling time-to-event distributions. We prove that the optimal variational distribution, 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 practically, we introduce CD-CVAE, a V-structure Variational Autoencoder (VAE) designed for the scalable implementation of CDVI. Further discussion extends some existing theories and training techniques to survival analysis. Extensive experiments validate our analysis and demonstrate significant improvements in the estimation of individual survival distributions.