In this work, we study the problem of clustering survival data $-$ a
challenging and so far under-explored task. We introduce a novel
semi-supervised probabilistic approach to cluster survival data by leveraging
recent advances in stochastic gradient variational inference. In contrast to
previous work, our proposed method employs a deep generative model to uncover
the underlying distribution of both the explanatory variables and censored
survival times. We compare our model to the related work on clustering and
mixture models for survival data in comprehensive experiments on a wide range
of synthetic, semi-synthetic, and real-world datasets, including medical
imaging data. Our method performs better at identifying clusters and is
competitive at predicting survival times. Relying on novel generative
assumptions, the proposed model offers a holistic perspective on clustering
survival data and holds a promise of discovering subpopulations whose survival
is regulated by different generative mechanisms.

本文介绍了一种基于半监督概率方法的生存数据聚类技术，使用了深度生成模型解决了未知基础变量和被检查的存活时间分布的问题，并在广泛的数据实验中取得了良好的效果和表现。

深度变分聚类生存数据

A Deep Variational Approach to Clustering Survival Data

Two popular classes of methods for approximate inference are Markov chain
Monte Carlo (MCMC) and variational inference. MCMC tends to be accurate if run
for a long enough time, while variational inference tends to give better
approximations at shorter time horizons. However, the amount of time needed for
MCMC to exceed the performance of variational methods can be quite high,
motivating more fine-grained tradeoffs. This paper derives a distribution over
variational parameters, designed to minimize a bound on the divergence between
the resulting marginal distribution and the target, and gives an example of how
to sample from this distribution in a way that interpolates between the
behavior of existing methods based on Langevin dynamics and stochastic gradient
variational inference (SGVI).

本文探讨不同近似推断方法（Markov chain Monte Carlo 和变分推断）的优缺点，并提出一种分布来衡量它们之间的差距，其示例介绍了如何从这个分布中采样，以便在现有方法（基于 Langevin 动力学和随机梯度变分推断）之间进行加权插值。

MCMC 和变分推断混合模型的分歧边界及其在朗之万动力学和 SGVI 中的应用

A Divergence Bound for Hybrids of MCMC and Variational Inference and an  Application to Langevin Dynamics and SGVI

Recent advances in stochastic gradient variational inference have made it
possible to perform variational Bayesian inference with posterior
approximations containing auxiliary random variables. This enables us to
explore a new synthesis of variational inference and Monte Carlo methods where
we incorporate one or more steps of MCMC into our variational approximation. By
doing so we obtain a rich class of inference algorithms bridging the gap
between variational methods and MCMC, and offering the best of both worlds:
fast posterior approximation through the maximization of an explicit objective,
with the option of trading off additional computation for additional accuracy.
We describe the theoretical foundations that make this possible and show some
promising first results.

提出了一种结合了变分推断和蒙特卡罗方法的新型推断算法，它通过在变分近似中引入一步或多步 MCMC 来生成具有随机辅助变量的后验分布近似，并通过在快速后验分布逼近和精度之间进行权衡提供了更好的灵活性和准确性。