ICML 2025

Survival Analysis via Density Estimation
Hiroki Yanagisawa 1 Shunta Akiyama 1
Abstract
This paper introduces a framework for survival
analysis by reinterpreting it as a form of density
estimation. Our algorithm post-processes density
estimation outputs to derive survival functions,
enabling the application of any density estimation
model to effectively estimate survival functions.
This approach broadens the toolkit for survival
analysis and enhances the flexibility and applica-
bility of existing techniques for density estimation.
Our framework is versatile enough to handle var-
ious survival analysis scenarios, including com-
peting risk models for multiple event types. It
can also address dependent censoring when prior
knowledge of the dependency between event time
and censoring time is available in the form of
a copula. In the absence of such information,
our framework can estimate the upper and lower
bounds of survival functions, accounting for the
associated uncertainty.
1. Introduction
Survival analysis constitutes a statistical methodology ex-
tensively employed across diverse domains, including
medicine, engineering, and social sciences, to analyze and
predict the probability distribution of the time until the oc-
currence of an event of interest. In numerous real-world
scenarios, the phenomenon of competing risks emerges
when an individual is subject to multiple mutually exclu-
sive events, where the occurrence of one event precludes
the observation or alters the probability of the other events.
The field of survival analysis with competing risks has a
rich historical foundation, as extensively reviewed in survey
papers (Wang et al., 2019; Wiegrebe et al., 2024).
Survival analysis with K competing risks can be conceptual-
ized as a variant of density estimation, a subfield of machine
learning aimed at estimating the probability distribution of a
1CyberAgent, Tokyo, Japan. Correspondence to: Hiroki Yanagi-
sawa <yanagisawa hiroki@cyberagent.co.jp>.
Proceedin...